Question

Rút gọn biểu thức:

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

Answer 1

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

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

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

Answer 2

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

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