c,
\(\dfrac{x^2}{2x-10}+\dfrac{25-10x}{2x-10}\\ =\dfrac{x^2-10x+5^2}{2\left(x-5\right)}=\dfrac{\left(x-5\right)\left(x-5\right)}{2\left(x-5\right)}\\ =\dfrac{x-5}{2}\)
d,
\(=\dfrac{2x}{x\left(x+2\right)}-\dfrac{8}{\left(x-2\right)\left(x+2\right)}+\dfrac{2}{x-2}\)
\(=\dfrac{2x^2-4x}{x\left(x-2\right)\left(x+2\right)}-\dfrac{8x}{x\left(x-2\right)\left(x+2\right)}+\dfrac{2x^2+4x}{x\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{2x^2-4x-8x+2x^2+4x}{x\left(x-2\right)\left(x+2\right)}=\dfrac{4x^2-8x}{x\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{4x\left(x-2\right)}{x\left(x-2\right)\left(x+2\right)}=\dfrac{4x}{x\left(x+2\right)}\)
