Thực hiện các phép tính sau: g) 2x/ 9-x^2+1/x-3-1/x+3 .

Trả lời

g, $\frac{2x}{9-x^2}+\frac{1}{x-3}-\frac{1}{x+3}$

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

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

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

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

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

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

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