Thực hiện các phép tính sau:

DẠNG THỰC HIỆN PHÉP TÍNH

$\Large{\frac{4xy(2x^2 - xy) + (8x^3y3 - 6x^4y^2 + 2xy)}{(2xy)}}$

$\Large{\frac{4xy(2x^2-xy)+(8x^3y^3 - 6x^4y^2 + 2xy)}{2xy}}$
=

$\Large{\frac{2xy(2.2x^2-2.xy) + 2xy(4x^2y^2 - 3x^2y^1 + 1xy)}{2xy}}$
Triệt tiêu thừa số chung: 2xy; rút gọn

$2.2x^2-2.xy$ và bỏ ngoặc, ta có:
A = (4x2−2xy) + (4x2y2−3x3y+1)
A = 4x2 − 2xy + 4x2y2 − 3x3y + 1

2)

$\Large{\frac{7x+6}{5x-1}+\frac{8x-9}{5x-1}}$ =

$\Large{\frac{7x+6+8x-9)}{5x-1}}$
=

$\Large{\frac{15x-3}{5x-1}}$
=

$\Large{\frac{3(5x-1)}{5x-1}}$
Triệt tiêu 5x - 1
= 3

3) (x - 5)2 + (x + 3)(2 - x)A =

$(x - 5)^2 + (x + 3)(2 - x)$
Mở rộng:

$(x−5)^2 = x^2 − 10x + 25$

$(x+3)(2−x): −x^2 − x + 6$

A =

$x^2 − 10x + 25 − x^2 − x + 6$
A =

$x^2−x^2−10x−x+25+6$
A =

$11x + 31$

$\Large{\frac{4}{x+2} - \frac{2}{x-2}+\frac{12x}{x^2 - 4}}$
A =

$\frac{4}{x+2}$ -

$\frac{2}{x-2}$ +

$\frac{12x}{x^2 - 4}$
Bội Số Chung Nhỏ Nhất của

$x + 2, x − 2, x^2 − 4$

là

$x^2 - 2^2$ =

$(x + 2)(x − 2)$

A =

$\Large{\frac{4 (x - 2) - 2 (x +2) + 12x}{x^2 - 4}}$
A =

$\Large{\frac{4x - 8 - 2x - 4 + 12x}{x^2-4}}$
A =

$\Large{\frac{- 12 + 14x}{x^2-4}}$ A =

$\Large{\frac{14x - 12}{x^2-4}}$

5)

$\Large{\frac{2xy(3x^2 - xy) + (6x^3y^3 - 12x^4y^2 + 3xy)}{ (3xy)}}$

A =

$\Large{\frac{2xy(3x^2 - xy) + (6x^3y^3 - 12x^4y^2 + 3xy)}{3xy}}$
Áp dụng quy tắc: a+(b+c) = a+b+c

$2xy(3x^2−xy)+(6x^2y^2.3−12x^4y^2+3xy)$
A =

$\Large{\frac{2xy(3x^2 − xy) + 6x^2y^2 − 12x^4y^2 + 3xy} {3xy}}$
Đặt xy làm thừa số chung, ta có:
A =

$\Large{\frac{xy(6x^2 - 2xy + 6xy -12x^3y + 3)} {3xy}}$
A =

$\Large{\frac{xy(6x^2 + 4xy - 12x^3y + 3)} {3xy}}$
Triệt tiêu x
A =

$\Large{\frac{xy(6x^2 + 4xy - 12x^3y + 3)} {3xy}}$

6)

$\Large{\frac{a-1}{a-2}+\frac{a-3}{a-2}}$
=

$\Large{\frac{(a -1)+(a -3)}{a-2}}$
=

$\Large{\frac{a -1+ a -3}{a -2}}$
=

$\Large{\frac{2a - 4}{a -2}}$
=

$\Large{\frac{2(a - 2)}{a -2}}$
` =

$2$

$(2x - 3)^2 + (x + 2)(1 - 4x)$ = 4x2 -12x + 9 + x - 4x2 +2 - 8x
= 4x2 - 4x2 -12x + x - 8x + 9 + 2 = - 19x +11

8)

$\Large{\frac{6x}{x^2-9}+\frac{5x}{x-3}+\frac{x}{x+3}}$
A=

$\Large{\frac{6x}{x^2-9}+\frac{5x}{x-3}+\frac{x}{x+3}}$
mà

${x^2-9}$ =

$(x+3)(x-3)$
A =

$\Large{\frac{6x}{(x+3)(x-3)}+\frac{5x(x+3)}{(x+3)(x-3)}+\frac{x(x-3)}{(x+3)(x-3)}}$
=

$\Large{\frac{6x}{(x+3)(x-3)}+\frac{5x^2 +15x }{(x+3)(x-3)}+\frac{x^2 -3x }{(x+3)(x-3)}}$
=

$\Large{\frac{6x + 5x^2 +15x + x^2 -3x }{(x+3)(x-3)}}$
=

$\Large{\frac{5x^2 + x^2 + 15x + 6x -3x }{(x+3)(x-3)}}$
=

$\Large{\frac{6x^2 + 18x}{(x+3)(x-3)}}$
=

$\Large{\frac{6x(x + 3)}{(x+3)(x-3)}}$
=

$\Large{\frac{6x}{x-3}}$

9)

$5xy(2x^2 - xy) + (10x^3y^3 + 15x^4y^2 - 5xy): (5xy)$
A =

$5xy(2x^2 - xy) + (10x^3y^3 + 15x^4y^2 - 5xy): (5xy)$

$(10x^3y^3 + 15x^4y^2 - 5xy): (5xy)$
=

$5xy(x^2y^2 + 3x^3y -1) : (5xy)$
Triệt tiêu 5xy
=

$x^2y^2 + 3x^3y -1$
A =

$5xy(2x^2 - xy) + x^2y^2 + 3x^3y -1$
A =

$10x^3y - 5x^2y^2 + x^2y^2 + 3x^3y -1$
A =

$13x^3y - 4x^2y^2 - 1$

10)

$\Large{\frac{3x-1}{x+2}+\frac{2x+11}{x+2}}$
A =

$\Large{\frac{3x-1 + 2x+11}{x+2}}$
A =

$\Large{\frac{5x +10}{x+2}}$
A =

$\Large{\frac{5(x +2)}{x+2}}$
Triệt tiêu x + 2
A = 5

11)

$(2x - 1)^2+ (4x + 2)(1 - x)$
A =

$(4x^2 - 4x +1) + (4x - 4x^2 + 2 - 2x)$
A =

$4x^2 - 4x +1 + 4x - 4x^2 + 2 - 2x$
A =

$4x^2 - 4x^2 - 4x + 4x - 2x +1 + 2$ A =

$-2x +3$

12)

$3x^2y(x^2 - 4y) + (30x^5y^3 - 25x^3y^4 - 5xy^2) : 5xy^2$

A =

$3x^2y(x^2 - 4y) + (30x^5y^3 - 25x^3y^4 - 5xy^2) : 5xy^2$
A =

$(3x^4y - 12x^2y^2) + 5xy^2(6x^4y - 5x^2y^2 - 1) : 5xy^2$
A =

$(3x^4y - 12x^2y^2) + (6x^4y - 5x^2y^2 - 1)$
A =

$3x^4y - 12x^2y^2 + 6x^4y - 5x^2y^2 - 1$
A =

$3x^4y + 6x^4y - 12x^2y^2 - 5x^2y^2 - 1$
A =

$9x^4y - 17x^2y^2 - 1$

13)

$\Large{\frac{11x}{2x-3}+ \frac{x-18}{2x-3}}$
A =

$\Large{\frac{11x + x - 18}{2x - 3}}$
A =

$\Large{\frac{12x - 18}{2x - 3}}$
A =

$\Large{\frac{6(x - 3)}{2x - 3}}$
Triệt tiêu 2x - 3
A = 6

14)

$(3x + 2)(3x - 2) + 9x(1 - x)$
1. Use Difference of Squares:

$a2−b2=(a+b)(a−b)$ .

$(3x)^2 − 2^2 + 9x(1 − x)$
2. Expand by distributing terms.

$(3x)^2 – 2^2 + 9x − 9x^2$
3. Use Multiplication Distributive Property:

$(xy)a=xaya$ .

$3^2x^2 − 2^2 + 9x − 9x^2$
4. Simplify

$3^2$ to 9.

$9x^2 – 2^2 + 9x − 9x^2$
5. Simplify

$2^2$ to 4.

$9x^2 – 4 + 9x − 9x^2$
6. Collect like terms.

$(9x^2 − 9x^2) – 4 + 9x$
7. Simplify.

$−4 + 9x$
8. Regroup terms.

$9x − 4$

15)

$\Large{\frac{x}{x+2}-\frac{3}{x-2}-\frac{x^2+9}{x^2-4}}$

$x^2 - 4 = (x - 2)(x + 2)$
A =

$\Large{\frac{x}{x+2}-\frac{3}{x-2}-\frac{x^2+9}{x^2-4}}$
A =

$\Large{\frac{x(x-2) - 3(x+2) - (x^2+9)}{(x - 2)(x + 2)}}$
A =

$\Large{\frac{x^2 - 2x - 3x - 6 - x^2 - 9)}{(x - 2)(x + 2)}}$
A =

$\Large{\frac{x^2 - x^2 - 2x - 3x - 6 - 9}{(x - 2)(x + 2)}}$
A =

$\Large{\frac{ - 5x - 15}{(x - 2)(x + 2)}}$
A =

$\Large{\frac{ - 5(x + 3)}{(x - 2)(x + 2)}}$

16)

$4x^2y(2xy^2 - xy)+ (25x^4y^3 - 10x^4y^4 + 5xy): (5xy)$
A =

$(8x^3y^3 - 4x^3y^3)+ (5xy(5x^3y^2 - 2x^3y^3 + 1)): (5xy)$
A =

$8x^3y^3 - 4x^3y^3+ 5x^3y^2 - 2x^3y^3 + 1$

A =

$8x^3y^3 - 4x^3y^3 - 2x^3y^3 + 5x^3y^2 + 1$
A =

$2x^3y^3 + 5x^3y^2 + 1$

17)

$\Large{\frac{2x-4}{3x+2}+\frac{3x+1}{3x+2}}$
A =

$\Large{\frac{2x - 4 + 3x+1}{3x+2}}$
A =

$\Large{\frac{5x - 3}{3x+2}}$

18)

$(x - 6)^2 + (x + 7)(4 - x)$
A =

$(x^2 - 12x + 36) + (4x - x^2 +28 - 7x)$
A =

$x^2 - 12x + 36 + 4x - x^2 +28 - 7x$

A =

$x^2 - x^2- 12x + 4x - 7x + 36 +28$
A =

$- 15x + 60$
A =

$- 15(x - 4)$

19)

$\Large{\frac{1-3x}{2x}+\frac{3x-2}{2x-1}-\frac{3x-2}{4x^2-2x}}$
A =

$\Large{\frac{1-3x}{2x}+\frac{3x-2}{2x-1}-\frac{3x-2}{4x^2-2x}}$

$4x^2-2x = 2x(2x -1)$

A =

$\Large{\frac{(1-3x)(2x -1)}{2x(2x -1)}+\frac{2x(3x-2)}{2x(2x-1)}-\frac{3x-2}{2x(2x -1)}}$

A =

$\Large{\frac{(1-3x)(2x -1) + 2x(3x-2) - (3x-2)}{2x(2x -1)}}$
A =

$\Large{\frac{(2x -1 - 6x^2 + 3x) + (6x^2 - 4x) - (3x-2)}{2x(2x -1)}}$
A =

$\Large{\frac{2x -1 - 6x^2 + 3x + 6x^2 - 4x - 3x + 2}{2x(2x -1)}}$
A =

$\Large{\frac{ - 6x^2 + 6x^2+ 3x + 2x - 4x - 3x + 2 -1}{2x(2x -1)}}$
A =

$\Large{\frac{ (- 6x^2 + 6x^2)+ (3x + 2x - 4x - 3x) + (2 -1)}{2x(2x -1)}}$
A =

$\Large{\frac{- 2x + 1 }{2x(2x -1)}}$
A =

$\Large{\frac{- (2x - 1) }{2x(2x -1)}}$
A =

$\Large{\frac{- 1 }{2x }}$

20)

$2xy(2x - xy^2) + (3x^4y^4 - 9x^4y^2 + 6x^2y): (3x^2y)$
A =

$(4x^2y - 2x^2y^3) + (3x^2y(x^2y^3 - 3x^2y + 2): (3x^2y)$
Triệt tiêu

$3x^2y$
A =

$(4x^2y - 2x^2y^3) + (x^2y^3 - 3x^2y + 2)$
A =

$4x^2y - 2x^2y^3 + x^2y^3 - 3x^2y + 2$ A =

$4x^2y - 3x^2y + x^2y^3 - 2x^2y^3 + 2$
A =

$- x^2y^3 + x^2y + 2$

21)

$\Large{\frac{x+2}{x-1}+\frac{3x+1}{x-1}}$
A =

$\Large{\frac{x + 2 + 3x + 1}{x-1}}$
A =

$\Large{\frac{5x + 3}{x-1}}$
A =

$27x -3$

22)

$5x(5 - x) + (x + 1)(5x - 3)$
A =

$(25x - 5x^2) + (5x^2 - 3x + 5x -3 )$
A =

$25x - 5x^2 + 5x^2 - 3x + 5x -3$
A =

$5x^2 - 5x^2 + 25x + 5x - 3x -3$
A =

$27x -3$

23)

$\Large{\frac{x}{x-2}-\frac{x}{x+2}-\frac{8}{x^2-4}}$

$x^2 - 4 = (x -2 ) (x + 2)$ A =

$\Large{\frac{x}{x-2}-\frac{x}{x+2}-\frac{8}{ (x -2 ) (x + 2)}}$
A =

$\Large{\frac{x(x+2) - x(x-2) - 8}{ (x -2 ) (x + 2)}}$
A =

$\Large{\frac{x^2 + 2x - x^2 + 2x - 8}{ (x -2 ) (x + 2)}}$
A =

$\Large{\frac{x^2 - x^2 + 2x + 2x - 8}{ (x -2 ) (x + 2)}}$
A =

$\Large{\frac{ 4x - 8}{ (x -2 ) (x + 2)}}$
A =

$\Large{\frac{ 4(x - 2)}{ (x -2 ) (x + 2)}}$
Triệt tiêu x-2
A =

$\Large{\frac{ 4}{ x + 2}}$

24)

$3y^2(2x^2 + xy) + (9x^2y^5 + 6x^3y^4 - 12xy^2): 3xy^2$ A

$(6x^2y^2 + 3xy^3) + (9x^2y^5 + 6x^3y^4 - 12xy^2): 3xy^2$

$(9x^2y^5 + 6x^3y^4 - 12xy^2): 3xy^2$
=

$3xy^2 (3xy^3 + 2x^2y^2 - 4): 3xy^2$
Triệt tiêu

$3xy^2$
=

$3xy^4 + 2x^2y^3 - 4$
A =

$3y^2(2x^2 + xy) + 3xy^4 + 2x^2y^3 - 4$
A =

$6x^2y^2 + 3xy^3 + 3xy^4 + 2x^2y^3 - 4$
A =

$6x^2y^2 + 3xy^3 + 3xy^4 + 2x^2y^3 - 4$

25)

$\Large{\frac{2x+3}{x+1}+\frac{3x-1}{x+1}}$
A =

$\Large{\frac{(2x+3)+(3x-1)}{x+1}}$
A =

$\Large{\frac{2x+3+3x-1}{x+1}}$
A =

$\Large{\frac{5x+2}{x+1}}$

26)

$(2x - 5)(2x + 5) - (1 - 2x)^2 - 4x$
A =

$((2x)^2 - 5^2) - (1 - 2x)^2 - 4x$
A =

$(4x^2 - 25) - (1^2 - 2.1.2x + (2x)^2 ) - 4x$
A =

$4x^2 - 25 - 1^2 + 2.1.2x - (2x)^2 - 4x$
A =

$4x^2 - 25 - 1 + 4x - 4x^2 - 4x$ A =

$(4x^2 - 4x^2) + (4x - 4x) - 25 - 1$
A =

$- 25 - 1$
A =

$- 26$

27)

$\Large{\frac{2}{x+1}+\frac{4}{x-1}-\frac{5x+1}{x^2-1}}$

$x^2-1$ =

$x^2-1^2$ =

$(x-1)(x+1)$
A =

$\Large{\frac{2}{x+1}+\frac{4}{x-1}-\frac{5x+1}{x^2-1}}$
A =

$\Large{\frac{2(x-1) + 4(x+1) - (5x+1)}{(x-1)(x+1)}}$
A =

$\Large{\frac{2x - 2 + 4x + 4 - 5x -1}{(x-1)(x+1)}}$ A

$\Large{\frac{2x + 4x - 5x - 2 + 4 -1}{(x-1)(x+1)}}$
A =

$\Large{\frac{x +1}{(x-1)(x+1)}}$
A =

$\Large{\frac{x +1}{(x-1)(x+1)}}$
Triệt tiêu x + 1
A =

$\Large{\frac{1}{(x - 1)}}$

28)

$5xy(4x^2 - xy) + (4x^5y^2 - 8x^4y^3 + 16x^2y): (4x^2y)$
$(4x^5y^2 - 8x^4y^3 + 16x^2y): (4x^2y)

= 4x^2y(x^3y - 2x^2y^2 + 4): (4x^2y)$

Triệt tiêu

$(4x^2y)$ =

$x^3y - 2x^2y^2 + 4$
A =

$5xy(4x^2 - xy) + (4x^5y^2 - 8x^4y^3 + 16x^2y): (4x^2y)$
A =

$5xy(4x^2 - xy) + x^3y - 2x^2y^2 + 4$
A =

$(20x^3y - 5x^2y^2) + x^3y - 2x^2y^2 + 4$
A =

$20x^3y - 5x^2y^2 + x^3y - 2x^2y^2 + 4$
A =

$(20x^3y + x^3y)- (5x^2y^2 + 2x^2y^2) + 4$
A =

$21x^3y - 7x^2y^2 + 4$

29)

$\Large{\frac{2x-1}{3x-2}+\frac{x+3}{3x-2}}$

A =

$\Large{\frac{2x-1}{3x-2}+\frac{x+3}{3x-2}}$
A =

$\Large{\frac{(2x-1)+(x+3)}{3x-2}}$
A =

$\Large{\frac{2x-1+x+3}{3x-2}}$
A =

$\Large{\frac{3x+2}{3x-2}}$

30)

$(x + 5)^2 - (x + 3). (x - 2)$
A =

$(x^2 + 2.5.x + 5^2) - (x^2 - 2x + 3x - 6)$
A =

$x^2 + 2.5.x + 5^2 - x^2 + 2x - 3x + 6$
A =

$(x^2 - x^2) + (2.5.x + 2x - 3x) + (5^2 + 6)$
A =

$9x + 31$

31)

$\Large{\frac{1}{x+2}+\frac{2}{x-2}-\frac{2x}{x^2-4}}$

$x^2 - 4$ =

$x^2 - 2^2$ =

$(x - 2)(x + 2)$
A =

$\Large{\frac{1}{x+2}+\frac{2}{x-2}-\frac{2x}{x^2-4}}$
A =

$\Large{\frac{1(x - 2) + 2(x + 2) - 2x}{(x - 2)(x + 2)}}$
A =

$\Large{\frac{x - 2 + 2x + 4 -2x}{(x - 2)(x + 2)}}$
A =

$\Large{\frac{x + 2}{(x - 2)(x + 2)}}$
Triệt tiêu x +2
A =

$\Large{\frac{1}{(x - 2)}}$

32)

$\Large{\frac{x^2 - 1}{x^2 + 4x}.\frac{2x}{x - 1}}$
A =

$\Large{\frac{x^2 - 1}{x^2 + 4x}.\frac{2x}{x - 1}}$

A =

$\Large{\frac{(x^2 - 1)2x}{(x^2 + 4x)(x - 1)}}$
A =

$\Large{\frac{2x^3 - 2x}{x^3 - x^2 + 4x^2 - 4x}}$
A =

$\Large{\frac{2x^3 - 2x}{x^3 + 3x^2 - 4x}}$
A =

$\Large{\frac{2x(x^2 - 1)}{x(x^2 + 3x - 4)}}$
Triệt tiêu x
A =

$\Large{\frac{2(x^2 - 1)}{(x^2 + 3x - 4)}}$

33)

$\Large{\frac{x+y}{xy}+\frac{x-2}{xy}+\frac{x-14}{x^2-4}}$

$x^2-4 = x^2 - 2^2$ =

$(x+2)(x-2)$

A =

$\Large{\frac{x+y}{xy}+\frac{x-2}{xy}+\frac{x-14}{x^2-4}}$
A =

$\Large{\frac{x+y}{xy}+\frac{x-2}{xy}+\frac{x-14}{x^2 - 2^2}}$
A =

$\Large{\frac{x+y}{xy}+\frac{x-2}{xy}+\frac{x-14}{(x+2)(x-2)}}$
MTC:

$xy(x+2)(x-2)$
A =

$\Large{\frac{(x+y)(x+2)(x-2)+(x-2)(x+2)(x-2)+(x-14)xy}{xy(x+2)(x-2)}}$

$x^ax^b = x^ab$
A =

$\Large{\frac{(x+y)(x+2)(x-2)+((x-2)(x-2))(x+2)+(x-14)xy}{xy(x+2)(x-2)}}$
A =

$\Large{\frac{(x+y)(x+2)(x-2)+(x-2)^2(x+2)+(x-14)xy}{xy(x+2)(x-2)}}$
A =

$\Large{\frac{x^3−2x^2+2x^2−4x+yx^2−2yx+2yx−4y+x3+2x^2−4x^2−8x+4x+8+x2y−14xy}{xy(x+2)(x-2)}}$
A =

$\Large{\frac{(x^3+x^3)+(−2x^2+2x^2+2x^2−4x^2)+(−4x−8x+4x)+(x^2y+x^2y)+(−2xy+2xy−14xy)−4y+8}{xy(x+2)(x-2)}}$

$(x^3+x^3)+(−2x^2+2x^2+2x^2−4x^2)+(−4x−8x+4x)+(x^2y+x^2y)+(−2xy+2xy−14xy)−4y+8$
=

$2x^3−2x^2−8x+2x^2y−14xy−4y+8$
A =

$\Large{\frac{2x^3−2x^2−8x+2x^2y−14xy−4y+8}{xy(x+2)(x-2)}}$
A =

$\Large{\frac{2(x^3−x^2−4x+x^2y−7xy−2y+4)}{xy(x+2)(x-2)}}$

34)

$\Large{\frac{x+1}{x-2}-\frac{x-2}{x+2}+\frac{x-14}{x^2-4}}$

$x^2-4 = x^2-2^2=(x+2)(x-2)$
A =

$\Large{\frac{x+1}{x-2}-\frac{x-2}{x+2}+\frac{x-14}{x^2-4}}$
A =

$\Large{\frac{x+1}{x-2}-\frac{x-2}{x+2}+\frac{x-14}{(x+2)(x-2)}}$

A =

$\Large{\frac{(x+1)(x+2)−(x−2)(x−2)+x−14}{(x+2)(x-2)}}$

$x^ax^b=x^{a+b}.$
A =

$\Large{\frac{(x+1)(x+2)−(x−2)^2+x−14}{(x+2)(x-2)}}$
A =

$\Large{\frac{x^2+2x+x+2−x^2+2x.2−2^2+x−14}{(x+2)(x-2)}}$

$2^2 = 4$ A =

$\Large{\frac{x^2+2x+x+2−x^2+2x.2−4+x−14}{(x+2)(x-2)}}$

$2x.2=4x$
A =

$\Large{\frac{x^2+2x+x+2−x^2+4x−4+x−14}{(x+2)(x-2)}}$
A =

$\Large{\frac{(x^2−x^2)+(2x+x+4x+x)+(2−4−14)}{(x+2)(x-2)}}$

$(x^2−x^2)+(2x+x+4x+x)+(2−4−14) = 8x−16$
A =

$\Large{\frac{8x−16}{(x+2)(x-2)}}$
A =

$\Large{\frac{8(x−2)}{(x+2)(x-2)}}$
Triệt tiêu x-2
A =

$\Large{\frac{8 }{(x+2) }}$

35)

$\Large{\frac{1}{x+5}-\frac{1}{x-5}+\frac{2x}{x^2-25}}$

$a^2-b^2; a=x, b=5$

$x^2-25 = x^2-5^2=(x+5)(x-5)$ A =

$\Large{\frac{1}{x+5}-\frac{1}{x-5}+\frac{2x}{x^2-25}}$
A =

$\Large{\frac{1}{x+5}-\frac{1}{x-5}+\frac{2x}{(x+5)(x-5)}}$
A =

$\Large{\frac{x−5−(x+5)+2x}{(x+5)(x-5)}}$
A =

$\Large{\frac{x−5−x-5+2x}{(x+5)(x-5)}}$
A =

$\Large{\frac{(x−x+2x)+(−5−5)}{(x+5)(x-5)}}$
A =

$\Large{\frac{(2x-10)}{(x+5)(x-5)}}$
A =

$\Large{\frac{(2(x-5))}{(x+5)(x-5)}}$
Triệt tiêu x-5
A =

$\Large{\frac{2)}{x+5}}$

36)

$6xy(2x^2 -3y)+(4x^2y^3 – 2x^4y^3 – 2x^4y^2 + 3xy):(xy)$ ?

37)

$\Large{\frac{a^2+2b}{a+3}+\frac{3a-2b}{a+3}}$
A =

$\Large{\frac{a^2+2b}{a+3}+\frac{3a-2b}{a+3}}$

A =

$\Large{\frac{a^2+2b+3a−2b}{a+3}}$
A =

$\Large{\frac{a(a+3)}{a+3}}$ A = a

38)

$(3x +1)^2 –(3x -2)(3x + 4)$

$(a+b)^2=a^2+2ab+b^2$
A =

$(3x +1)^2 –(3x -2)(3x + 4)$
A =

$(3x)^2+2×3x+1−(3x−2)(3x+4)$
A =

$(3x)^2+2×3x+1−(9x^2+12x−6x−8)$
A =

$(3x)^2+2×3x+1−9x^2-12x+6x+8)$

$(xy)^a=x^ay^a.$
A =

$32x^2+2×3x+1−9x^2−12x+6x+8$

$3^2=9$
A =

$9x^2+2×3x+1−9x^2−12x+6x+8$

$2.3x = 6x$
A =

$9x^2+6x+1−9x^2−12x+6x+8$
A =

$(9x^2−9x^2)+(6x−12x+6x)+(1+8)$
A = 9

39)

$\Large{\frac{x+1}{x-2}+\frac{4}{x+2}+\frac{2-7x}{x^2-4}}$

$a^2 - b^2 =(a+b)(a-b)$
a = x; b = 2

$x^2 − 2^2 = (x + 2)(x - 2)$

$\Large{\frac{x+1}{x−2}+\frac{4x}{x+2}+\frac{2−7x}{x^2−2^2}}$

$\Large{\frac{x+1}{x−2}+\frac{4x}{x+2}+\frac{2−7x}{(x + 2)(x - 2)}}$

$\Large{\frac{(x+1)(x+2)+4x(x−2)+2−7x}{(x + 2)(x - 2)}}$

$\Large{\frac{x^2+2x+x+2+4x^2−8x+2−7x}{(x + 2)(x - 2)}}$

$\Large{\frac{(x^2+4x^2)+(2x+x−8x−7x)+(2+2)}{(x + 2)(x - 2)}}$

$\Large{\frac{(5x^2−12x+4}{(x + 2)(x - 2)}}$

$\Large{\frac{5x^2−2x−10x+4}{(x + 2)(x - 2)}}$

$\Large{\frac{x(5x−2)−2(5x−2)}{(x + 2)(x - 2)}}$

$\Large{\frac{(5x−2)(x−2)}{(x + 2)(x - 2)}}$

$\Large{\frac{5x−2}{(x + 2)(x - 2)}}$

40)

$5a^2b(2a - ab^2) + (9a^5b^5 – 12a^5b^3 + 15a^2b^2): (3a^2b^2)$

41)

$\Large{\frac{5x-2}{4x+12}+\frac{x+9}{4x+12}}$

42)

$(2x + l)^2 - (2x + 3)(x - 1)$

43)

$\Large{\frac{1}{x+5}+\frac{6}{x-5}-\frac{2x}{x^2-25}}$

44)

$3x (2x^2y+ 3xy) + (6x^4y^2 - 8x^3y^2 + 4xy) : (2xy)$

45)

$\Large{\frac{x^2-2x}{x+3}:\frac{x^2-4}{x^2+3x}}$

46)

$(x - 3)(x + 3) + (x - 5)^2 - 2x(x - 5)$

47)

$\Large{\frac{5x+6}{x^2-4}+\frac{2}{x+2}-\frac{4}{x-2}}$

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