Question

simplify. \\(\frac{4u^2 - 20u + 24}{u^2 + 2u - 8}\\)

Explanation:

Step1: Factor numerator and denominator

Factor \(4u^2 - 20u + 24\): First, factor out 4: \(4(u^2 - 5u + 6)\). Then factor the quadratic: \(4(u - 2)(u - 3)\).
Factor \(u^2 + 2u - 8\): Find two numbers that multiply to -8 and add to 2, which are 4 and -2. So, \((u + 4)(u - 2)\).

Step2: Cancel common factors

The expression becomes \(\frac{4(u - 2)(u - 3)}{(u + 4)(u - 2)}\). Cancel the common factor \((u - 2)\) (assuming \(u
eq 2\)).

Step3: Simplify the expression

After canceling, we get \(\frac{4(u - 3)}{u + 4}\) or \(\frac{4u - 12}{u + 4}\).

Answer:

\(\frac{4(u - 3)}{u + 4}\) (or \(\frac{4u - 12}{u + 4}\))