Question

\(\dfrac{-3}{x+2}\) \(-\)\(\dfrac{2}{x-2}\) + \(\dfrac{4x}{x^2-4}\) (với x \(\ne\) 2 và x \(\ne\) \(-\) 2).

a Rút gọn biểu thức B.

b Tìm x để  B = \(\dfrac{1}{4}\)

Answer 1

\(=\dfrac{-3\left(x-2\right)-2\left(x+2\right)+4x}{x^2-4}\)

\(=\dfrac{-3x+6-2x-4+4x}{x^2-4}\)

\(=\dfrac{-x+2}{\left(x-2\right)\left(x+2\right)}\)

\(=\dfrac{-\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\)

\(=-\dfrac{1}{x+2}\left(x\ne2;x\ne-2\right)\)

Answer 2

\(\dfrac{-3}{x+2}-\dfrac{2}{x-2}+\dfrac{4x}{x^2-4}\left(x\ne\pm2\right)\)

\(=\dfrac{-3\left(x-2\right)-2\left(x+2\right)+4x}{\left(x-2\right)\left(x+2\right)}\)

\(=\dfrac{-3x+6-2x-4+4x}{\left(x-2\right)\left(x+2\right)}\)

\(=\dfrac{-x+2}{\left(x-2\right)\left(x+2\right)}\)

\(=-\dfrac{1}{x+2}\)