Question

\(\dfrac{x+1}{x-2}\) + \(\dfrac{x-2}{x+2}\) + \(\dfrac{x-14}{x^2-4}\)
Help tui ;------;

 

Answer 1

\(=\dfrac{x^2+3x+2+x^2-4x+4+x-14}{\left(x-2\right)\left(x+2\right)}=\dfrac{2x^2-8}{x^2-4}=\dfrac{2\left(x^2-4\right)}{x^2-4}=2\)

Answer 2

\(\dfrac{x+1}{x-2}+\dfrac{x-2}{x+2}+\dfrac{x-14}{x^2-4}\)

\(=\dfrac{x+1}{x-2}+\dfrac{x-2}{x+2}+\dfrac{x-14}{\left(x+2\right)\left(x-2\right)}\)

\(=\dfrac{\left(x+2\right)\left(x+1\right)+\left(x-2\right)\left(x-2\right)+x-14}{\left(x+2\right)\left(x-2\right)}\)

\(=\dfrac{x^2+x+2x+2+x^2-2x-2x+4+x-14}{\left(x+2\right)\left(x-2\right)}\)

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