Question: Simplify. \frac{4u + 32}{3u^2 + 24u}

Solution

To simplify the expression \(\frac{4u + 32}{3u^2 + 24u}\), we need to factor both the numerator and the denominator. First, factor the numerator \(4u + 32\). The greatest common factor (GCF) of the terms in the numerator is 4. Factor out 4: \[ 4u + 32 = 4(u + 8) \] Next, factor the denominator \(3u^2 + 24u\). The greatest common factor (GCF) of the terms in the denominator is 3u. Factor out 3u: \[ 3u^2 + 24u = 3u(u + 8) \] Now, substitute the factored forms back into the fraction: \[ \frac{4(u + 8)}{3u(u + 8)} \] Cancel the common factor \((u + 8)\) from the numerator and the denominator: \[ \frac{4}{3u} \] The simplified form of the expression is \(\frac{4}{3u}\).