Question

1/x^2+x-2-x/x+1

e)x/2a-b-4ax/4a^2-b^2+b/2a+b

Answer 1

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

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

e: \(=\dfrac{x}{2a-b}-\dfrac{4ax}{\left(2a-b\right)\left(2a+b\right)}+\dfrac{b}{2a+b}\)

\(=\dfrac{2ax+bx-4ax+2ab-b^2}{\left(2a+b\right)\left(2a-b\right)}\)

\(=\dfrac{-b^2+2ab-2ax+bx}{\left(2a+b\right)\left(2a-b\right)}\)

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