Không giải tắt, giải đầy đủ và lấy 60 điểm

Đáp án+Giải thích các bước giải:

a) $\frac{x+1}{2x+6}+$ $\frac{2x+3}{x^2+3x}$ 

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

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

$=\frac{x^2+x+4x+6}{2x(x+3)}$

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

$=\frac{(x+2)(x+3)}{2x(x+3)}$

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

b) $\frac{3}{2x + 6}-$ $\frac{x-6}{2x^2+6x}$

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

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

$=\frac{2x+6}{x(2x+6)}$

$=\frac{1}{x}$

c) $\frac{x}{x-2y}+$ $\frac{x}{x+2y}+$ $\frac{4xy}{4y^2-x^2}$

$=\frac{x(x+2y)+x(x-2y)-4xy}{(x-2y)(x+2y)}$

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

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

$=\frac{2x(x-2y)}{(x-2y)(x+2y)}$

$=\frac{2x}{x+2y}$

d) $\frac{1}{3x-2}-$ $\frac{1}{3x+2}-$ $\frac{3x-6}{4-9x^2}$

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

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

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

$=\frac{1}{3x+2}$

g) $\frac{x^2-36}{2x+10}.$ $\frac{3}{6-y}$

$=\frac{(x-6)(x+6).3}{2(x+5)(6-x)}$

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

h) $\frac{1-4x^2}{x^2+4x}:$ $\frac{2-4x}{3x}$

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

$=\frac{(1-2x)(1+2x).3}{(x+4).2(1-2x)}$

$=\frac{3(1+2x)}{2(x+4)}$