Question

simplify. $\frac{x^{2}-9x + 14}{x^{2}+5x - 14}$ -4x $\frac{x - 7}{x + 7}$ $\frac{x + 5}{x - 9}$ 4x

Explanation:

Step1: Factor the polynomials

Factor $x^{2}-9x + 14=(x - 2)(x - 7)$ and $x^{2}+5x-14=(x + 7)(x - 2)$.
So the expression becomes $\frac{(x - 2)(x - 7)}{(x + 7)(x - 2)}$.

Step2: Cancel out common factors

Cancel out the common factor $(x - 2)$ in the numerator and denominator.
We get $\frac{x - 7}{x + 7}$.

Answer:

$\frac{x - 7}{x + 7}$