Question

m)(\(\dfrac{2x}{x^2-1}\)+\(\dfrac{x-1}{2x+2}\)):\(\dfrac{x+1}{2x}\)+\(\dfrac{3}{1-x}\)
p)(\(\dfrac{2+x}{2-x}\)+\(\dfrac{4x^2}{x^2-4}\)-\(\dfrac{2-x}{2+x}\)):\(\dfrac{x^2-3x}{2x^2-x^3}\)

Answer 1

m: \(=\left(\dfrac{2x}{\left(x-1\right)\left(x+1\right)}+\dfrac{x-1}{2\left(x+1\right)}\right)\cdot\dfrac{2x}{x+1}-\dfrac{3}{x-1}\)

\(=\dfrac{4x+x^2-2x+1}{2\left(x-1\right)\left(x+1\right)}\cdot\dfrac{2x}{x+1}-\dfrac{3}{x-1}\)

\(=\dfrac{\left(x+1\right)^2\cdot x}{\left(x-1\right)\left(x+1\right)^2}-\dfrac{3}{x-1}=\dfrac{x}{x-1}-\dfrac{3}{x-1}=\dfrac{x-3}{x-1}\)

p: \(=\left(\dfrac{-\left(x+2\right)}{x-2}+\dfrac{4x^2}{\left(x-2\right)\left(x+2\right)}+\dfrac{x-2}{x+2}\right)\cdot\dfrac{-x^2\left(x-2\right)}{x\left(x-3\right)}\)

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

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