Question

1. rút gọn

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

Answer 1

Lời giải:

ĐKXĐ: \(x\neq -3; x\neq \pm 6; x\neq 0\)

Ta có:

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

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

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

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

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

\(=\frac{x^2-(x+6)^2-x(2x+6)}{(x+6)(2x+6)}=\frac{-(2x^2+18x+36)}{2x^2+18x+36}=-1\)