Thực hiện các phép tính sau: b) 1/x+5-1/x-5+2x/x^2-25 ;

Trả lời

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

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

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

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

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

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

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