Ta có:\(\left(\frac{6}{x^2-6x}+\frac{1}{x+6}\right):\frac{x^2+36}{x^2-36}\)

   \(=\left(\frac{6\left(x+6\right)}{x\left(x-6\right)\left(x+6\right)}+\frac{x\left(x-6\right)}{x\left(x-6\right)\left(x+6\right)}\right).\frac{x^2-6^2}{x^2+36}\)

     \(=\left(\frac{6x+36+x^2-6x}{x\left(x-6\right)\left(x+6\right)}\right).\frac{\left(x-6\right)\left(x+6\right)}{x^2+36}\)

        \(=\frac{x^2+36}{x\left(x-6\right)\left(x+6\right)}.\frac{\left(x-6\right)\left(x+6\right)}{x^2+36}\)

      \(=\frac{1}{x}\)

Kiểm tra đi bạn phải là \(\frac{1}{x}\)

công trừ nhân phia phân thwscc đi

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

\(\left(\frac{x}{x^2-36}-\frac{x-6}{x^2+6x}\right):\frac{2x-6}{x^2+6x}+\frac{x}{6-x}\\ =\left(\frac{x}{\left(x-6\right)\left(x+6\right)}-\frac{x-6}{x\left(x+6\right)}\right).\frac{x\left(x+6\right)}{2x-6}+\frac{-x}{x-6}\\ =\left(\frac{x^2}{x\left(x-6\right)\left(x+6\right)}-\frac{\left(x-6\right)^2}{x\left(x-6\right)\left(x+6\right)}\right).\frac{x\left(x+6\right)}{2x-6}+\frac{-x}{x-6}\\ =\frac{\left(x-x+6\right)\left(x+x-6\right)}{x\left(x-6\right)\left(x+6\right)}.\frac{x\left(x+6\right)}{2x-6}+\frac{-x}{x-6}\\ =\frac{6\left(2x-6\right)}{x\left(x-6\right)\left(x+6\right)}.\frac{x\left(x+6\right)}{2x-6}+\frac{-x}{x-6}\\ =\frac{6x\left(2x-6\right)\left(x+6\right)}{x\left(x-6\right)\left(x+6\right)\left(2x-6\right)}+\frac{-x}{x-6}\\ =\frac{6}{x-6}+\frac{-x}{x-6}\\ =\frac{6-x}{x-6}\\ =-1\left(đpcm\right)\)

\(\left(\frac{x}{x^2-36}+\frac{6-x}{x^2+6x}\right):\frac{2x-6}{x^2+6x}+\frac{x}{6-x}\)

đkxđ: \(x\ne0;x\ne\pm6\)

MTC=x(x+6)(x-6)

\(=\left[\frac{x}{\left(x+6\right)\left(x-6\right)}+\frac{6-x}{x\left(x+6\right)}\right]\cdot\frac{x\left(x+6\right)}{x\left(x-3\right)}-\frac{x}{x-6}\)

\(=\left[\frac{x^2}{x\left(x^2-36\right)}-\frac{\left(x-6\right)^2}{x\left(x^2-36\right)}\right]\cdot\frac{x\left(x+6\right)}{x\left(x-3\right)}-\frac{x}{x-6}\)

\(=\frac{12\left(x-3\right)}{x\left(x+6\right)\left(x-6\right)}\cdot\frac{x\left(x+6\right)}{x\left(x-3\right)}-\frac{x}{x-6}\)

\(=\frac{12}{x\left(x-6\right)}-\frac{x^2}{x\left(x-6\right)}\)

\(=\frac{12-x^2}{x\left(x-6\right)}\)

.....................

A = \(\left(\frac{x}{x^2-36}-\frac{x-6}{x^2+6x}\right):\frac{2x-6}{x^2+6x}+\frac{x}{6-x}\)

= \(\left[\frac{x}{\left(x-6\right)\left(x+6\right)}-\frac{x-6}{x\left(x+6\right)}\right]:\frac{2\left(x-3\right)}{x\left(x+6\right)}-\frac{x}{x-6}\)

= \(\left[\frac{x^2}{x\left(x-6\right)\left(x+6\right)}-\frac{\left(x-6\right)^2}{x\left(x-6\right)\left(x+6\right)}\right]:\frac{2\left(x-3\right)}{x\left(x+6\right)}-\frac{x}{x-6}\)

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

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

=

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

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

= \(\frac{x}{x-6}-\frac{x}{x-6}\)

= 0

\(a)A=(\frac{x}{(x+6)(x+6)}-\frac{x-6}{x(x+6)})\cdot\frac{x(x+6)}{2x-6}+\frac{x}{x-6}\)

\(A=\frac{x^2-(x-6)^2}{x(x+6)(x-6)}\cdot\frac{x(x+6)}{2x-6}-\frac{x}{x-6}=\frac{(x-x+6)(x+x-6)}{(x-6)(2x-6)}-\frac{x}{x-6}\)

\(=\frac{6(2x-6)}{(x-6)(2x-6)}-\frac{x}{x-6}=\frac{6}{(x-6)}-\frac{x}{x-6}\cdot\frac{6-x}{x-6}=-1\)

\(b)\text{A luôn = -1 với mọi x}\)