Câu hỏi của hảo hảo

Question

x/(x-3 ) - 2/(x+3) + (x(1-x))/(x^2-9)

Nguyễn Việt Hoàng · Accepted Answer

$\frac{x}{x-3}-\frac{2}{x+3}+\frac{x\left(1-x\right)}{x^2-9}$

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

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

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

$=\frac{x\left(7-x\right)}{\left(x-3\right)\left(x+3\right)}=\frac{7x-x^2}{\left(x-3\right)\left(x+3\right)}$

Câu trả lời:

$\frac{x}{x-3}-\frac{2}{x+3}+\frac{x\left(1-x\right)}{x^2-9}$

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

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

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

$=\frac{x\left(7-x\right)}{\left(x-3\right)\left(x+3\right)}=\frac{7x-x^2}{\left(x-3\right)\left(x+3\right)}$