Giải Bài 3 trang 35

Đề bài

Thực hiện các phép tính sau:

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

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

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

Lời giải chi tiết

a) ĐKXĐ: $x\ne 1$

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

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

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

$=\frac{9-x}{x-1}$

b) ĐKXĐ: $x\ne \pm 5$

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

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

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

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

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

$=\frac{2}{x+5}$  

c) ĐKXĐ: $x\ne -y$

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

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

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

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