Question

1/x+2 + 5/x-2 - 2x/x^2-4

 

 

Answer 1

\(\dfrac{1}{x+2}+\dfrac{5}{x-2}-\dfrac{2x}{x^2-4}\)

\(\dfrac{x-2}{\left(x-2\right)\left(x+2\right)}+\dfrac{5x+10}{\left(x-2\right)\left(x+2\right)}-\dfrac{2x}{\left(x-2\right)\left(x+2\right)}\)

\(\dfrac{x-2+5x+10-2x}{\left(x-2\right)\left(x+2\right)}=\dfrac{8+4x}{\left(x-2\right)\left(x+2\right)}=\dfrac{4\left(2+x\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{4}{x-2}\)