Giải bài 6.22 trang 19

Đề bài

Thực hiện các phép tính sau:

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

$b)\frac{2x-1}{x}+\frac{1-x}{2x+1}+\frac{3}{x^2-9}+\frac{1-2x}{x}+\frac{x-1}{2x+1}-\frac{3}{x+3}$

Lời giải chi tiết

$\begin{array}{c}a)\frac{1}{x}+\frac{2}{x+1}+\frac{3}{x+2}-\frac{1}{x}-\frac{2}{x-1}-\frac{3}{x+2}\\ =\left(\frac{1}{x}-\frac{1}{x}\right)+\left(\frac{2}{x+1}-\frac{2}{x-1}\right)+\left(\frac{3}{x+2}-\frac{3}{x+2}\right)\\ =0+\frac{2}{x+1}-\frac{2}{x-1}+0\\ =\frac{2\left(x-1\right)-2\left(x+1\right)}{\left(x+1\right)\left(x-1\right)}=\frac{2x-2-2x-2}{\left(x+1\right)\left(x-1\right)}=\frac{-4}{\left(x+1\right)\left(x-1\right)}\end{array}$

$\begin{array}{c}b)\frac{2x-1}{x}+\frac{1-x}{2x+1}+\frac{3}{x^2-9}+\frac{1-2x}{x}+\frac{x-1}{2x+1}-\frac{3}{x+3}\\ =\left(\frac{2x-1}{x}+\frac{1-2x}{x}\right)+\left(\frac{1-x}{2x+1}+\frac{x-1}{2x+1}\right)+\left(\frac{3}{x^2-9}-\frac{3}{x+3}\right)\\ =0+0+\frac{3}{\left(x+3\right)\left(x-3\right)}-\frac{3}{x+3}\\ =\frac{3-3\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}=\frac{12-3x}{\left(x+3\right)\left(x-3\right)}\end{array}$