Question

Rút gọn: C= \(\left(\dfrac{1}{x+2}-\dfrac{2}{2-x}+\dfrac{x}{x^2-4}\right):\left(\dfrac{10-x^2}{x+2}-2+x\right)\)

Answer 1

\(C=\left(\dfrac{1}{x+2}-\dfrac{2}{2-x}+\dfrac{x}{x^2-4}\right):\left(\dfrac{10-x^2}{x+2}-2+x\right)\)

\(C=\left(\dfrac{1}{x+2}+\dfrac{2}{x-2}+\dfrac{x}{\left(x+2\right)\left(x-2\right)}\right):\left(\dfrac{10-x^2+x^2-4}{x+2}\right)\)

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

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

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

\(C=\dfrac{4x+2}{\left(x-2\right).6}\) = \(\dfrac{4x+2}{6x-12}\)