Question

( -a^3 - a^2 + a + 1) / ( -a^3 + a^2 + a - 1)

Answer 1

$\dfrac{-a^3 - a^2 + a + 1}{-a^2 + a^2 + a - 1} \\ \\ \\ \dfrac{-((a - 1)(a + 1)^2)}{-((a + 1)(a - 1)^2)} \\ \\ \\ \dfrac{-((a - 1)(\not a + \not)^\not ^2)}{-((a + 1)(\not a - \not1)^\not ^2)} \\ \\ \\ \dfrac{-(a - 1)}{-(a + 1)} \\ \\ \\ => \dfrac{a + 1}{a -1}$