Question

[Duong Thi Nhuong]

Rút gọn \(\left[\dfrac{x}{2x-6}-\dfrac{x^2}{x^2-9}+\dfrac{x}{2x-9}.\left(\dfrac{3}{x}-\dfrac{1}{x-3}\right)\right]:\dfrac{x^2-5x-6}{18-2x^2}\)

Answer 1

[Nguyen Thi Trinh]

ĐKXĐ: \(x\ne\pm3,x\ne\dfrac{9}{2}\)

= \(\left[\dfrac{x}{2\left(x-3\right)}-\dfrac{x^2}{\left(x-3\right)\left(x+3\right)}+\dfrac{x}{2x-9}.\dfrac{3\left(x-3\right)-x}{x\left(x-3\right)}\right]\) : \(\dfrac{x^2-5x-6}{-2\left(x-3\right)\left(x+3\right)}\)

= \(\left[\dfrac{x}{2\left(x-3\right)}-\dfrac{x^2}{\left(x-3\right)\left(x+3\right)}+\dfrac{1}{x-3}\right]:\dfrac{-\left(x^2-5x-6\right)}{2\left(x-3\right)\left(x+3\right)}\)

= \(\dfrac{x\left(x+3\right)-2x^2+2\left(x+3\right)}{2\left(x-3\right)\left(x+3\right)}:\dfrac{-\left(x^2-5x-6\right)}{2\left(x-3\right)\left(x+3\right)}\)

= \(\dfrac{-2\left(x^2-5x-6\right)\left(x-3\right)\left(x+3\right)}{-2\left(x^2-5x-6\right)\left(x-3\right)\left(x+3\right)}=1\)