Question

\(\frac{x-2}{x+2}-\frac{3}{x-2}=\frac{2\left(x-11\right)}{x^2-4}\)

Answer 1

\(\frac{x-2}{x+2}\)\(-\frac{3}{x-2}\)=\(\frac{2\left(x-11\right)}{x^2-4}\)

⇔\(\frac{\left(x-2\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}\)\(-\frac{3\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\)=\(\frac{2\left(x-11\right)}{x^2-4}\)

⇔\(\frac{x^2-2x-2x+4}{\left(x+2\right)\left(x-2\right)}\)-\(\frac{3x+6}{\left(x-2\right)\left(x+2\right)}\)=\(\frac{2x-22}{\left(x+2\right)\left(x-2\right)}\)

➞ \(x^2-2x-2x+4-3x-6=2x-22\)

⇔\(x^2-2x-2x-3x-2x=-4+6-22\)

⇔\(x^2-9x=-20\)

⇔\(x\left(x-9\right)=-20\)

⇔\(x=-20\) hoặc \(x-9=-20\)

⇔x = \(-20\) hoặc x= \(-11\)