Question: Simplify. \frac{6u^2 - 9u}{3u^2 - 21u}

Solution

To simplify the given ratio of polynomials using GCF factoring, we start with the expression: \[ \frac{6u^2 - 9u}{3u^2 - 21u} \] First, factor the greatest common factor (GCF) from the numerator \(6u^2 - 9u\). The GCF of \(6u^2\) and \(-9u\) is \(3u\). \[ 6u^2 - 9u = 3u(2u - 3) \] Next, factor the GCF from the denominator \(3u^2 - 21u\). The GCF of \(3u^2\) and \(-21u\) is \(3u\). \[ 3u^2 - 21u = 3u(u - 7) \] Now substitute the factored forms back into the original expression: \[ \frac{3u(2u - 3)}{3u(u - 7)} \] Cancel the common factor \(3u\) from the numerator and the denominator: \[ \frac{2u - 3}{u - 7} \] The simplified form of the expression is: \[ \frac{2u - 3}{u - 7} \]