Question

X^3-x^2-x+1/x^4-2x^2+1

Answer 1

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

Answer 2

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