Question

Thực hiện phép tính: x/x^2-4 +2/2-x +1/x+2

Answer 1

\(\dfrac{x}{x^2-4}+\dfrac{2}{2-x}+\dfrac{1}{x+2}\)

\(=\dfrac{x}{x^2-4}-\dfrac{2}{x-2}+\dfrac{1}{x+2}\)

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

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

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

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

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

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