Learn how to solve factorization problems step by step online. Simplify (x^4-2x^3x^2)/(x-1)+x+-1. Combine all terms into a single fraction with x-1 as common denominator. When multiplying two powers that have the same base (x-1), you can add the exponents. We can factor the polynomial x^4-2x^3+x^2+\left(x-1\right)^2 using the rational root theorem, which guarantees that for a polynomial of the form a_nx^n+a_{n-1}x^{n-1}+\dots+a_0 there is a rational root of the form \pm\frac{p}{q}, where p belongs to the divisors of the constant term a_0, and q belongs to the divisors of the leading coefficient a_n. List all divisors p of the constant term a_0, which equals 0. Next, list all divisors of the leading coefficient a_n, which equals 1.

Simplify (x^4-2x^3x^2)/(x-1)+x+-1