Question

Answer 1

c.

\(\dfrac{x^2}{2x-10}+\dfrac{25-10x}{2x-10}=\dfrac{x^2-10x+25}{2x-10}=\dfrac{\left(x-5\right)^2}{2\left(x-5\right)}=\dfrac{x-5}{2}\)

d.

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

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

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