Bài 3 trang 35 SGK Toán 8 Chân trời sáng tạo Tập 1 - KNTT

a) Ta có: $\frac{x+2}{x-1}-\frac{x-3}{x-1}+\frac{x-4}{1-x}$

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

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

$=\frac{5-\left(x-4\right)}{x-1}=\frac{5-x+4}{x-1}=\frac{9-x}{x-1}$

b) Ta có: $\frac{1}{x+5}-\frac{1}{x-5}+\frac{2x}{x^2-25}$

$=\frac{1}{x+5}-\frac{1}{x-5}+\frac{2x}{\left(x+5\right)\left(x-5\right)}$

$=\frac{x-5}{\left(x+5\right)\left(x-5\right)}-\frac{x+5}{\left(x+5\right)\left(x-5\right)}+\frac{2x}{\left(x+5\right)\left(x-5\right)}$

$=\frac{x-5-\left(x+5\right)+2x}{\left(x+5\right)\left(x-5\right)}$

$=\frac{x-5-x-5+2x}{\left(x+5\right)\left(x-5\right)}$

$=\frac{2x-10}{\left(x+5\right)\left(x-5\right)}$

$=\frac{2\left(x-5\right)}{\left(x+5\right)\left(x-5\right)}=\frac{2}{x+5}$

c) Ta có: $x+\frac{2y^2}{x+y}-y$

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

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

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

-- Mod Toán 8 HỌC247