Xem lại đề gõ thiếu không? Ở \(\frac{2x-6}{x^2+6}\) phải là \(\frac{2x-6}{x^2+6x}\) chứ nhỉ
Sửa lại đề của bạn nhé
\(\left(\frac{x}{x^2-36}-\frac{x-6}{x^2+6x}\right):\frac{2x-6}{x^2+6x}+\frac{x}{6-x}\\ =\left(\frac{x}{\left(x-6\right)\left(x+6\right)}-\frac{x-6}{x\left(x+6\right)}\right).\frac{x\left(x+6\right)}{2x-6}+\frac{-x}{x-6}\\ =\left(\frac{x^2}{x\left(x-6\right)\left(x+6\right)}-\frac{\left(x-6\right)^2}{x\left(x-6\right)\left(x+6\right)}\right).\frac{x\left(x+6\right)}{2x-6}+\frac{-x}{x-6}\\ =\frac{\left(x-x+6\right)\left(x+x-6\right)}{x\left(x-6\right)\left(x+6\right)}.\frac{x\left(x+6\right)}{2x-6}+\frac{-x}{x-6}\\ =\frac{6\left(2x-6\right)}{x\left(x-6\right)\left(x+6\right)}.\frac{x\left(x+6\right)}{2x-6}+\frac{-x}{x-6}\\ =\frac{6x\left(2x-6\right)\left(x+6\right)}{x\left(x-6\right)\left(x+6\right)\left(2x-6\right)}+\frac{-x}{x-6}\\ =\frac{6}{x-6}+\frac{-x}{x-6}\\ =\frac{6-x}{x-6}\\ =-1\left(đpcm\right)\)
