Question

simplify the expression completely if possible.\\(\frac{2x^2 + 16x}{x^2 - 9x + 18}\\)

Explanation:

Step1: Factor numerator

Factor out $2x$ from terms.
$2x^2 + 16x = 2x(x + 8)$

Step2: Factor denominator

Factor quadratic into binomials.
$x^2 - 9x + 18 = (x - 3)(x - 6)$

Step3: Check for common factors

No shared factors to cancel.
$\frac{2x(x + 8)}{(x - 3)(x - 6)}$

Answer:

$\frac{2x(x + 8)}{(x - 3)(x - 6)}$ (or expanded form $\frac{2x^2 + 16x}{x^2 - 9x + 18}$ is also acceptable as no further simplification is possible)