Question

simplify the expression completely if possible.
\frac{x^{2}+2x - 24}{x^{2}+3x - 28}

Explanation:

Step1: Factor the numerator

Factor $x^{2}+2x - 24$. We need two numbers that multiply to $-24$ and add up to $2$. The numbers are $6$ and $- 4$. So $x^{2}+2x - 24=(x + 6)(x-4)$.

Step2: Factor the denominator

Factor $x^{2}+3x - 28$. We need two numbers that multiply to $-28$ and add up to $3$. The numbers are $7$ and $-4$. So $x^{2}+3x - 28=(x + 7)(x-4)$.

Step3: Simplify the fraction

$\frac{x^{2}+2x - 24}{x^{2}+3x - 28}=\frac{(x + 6)(x-4)}{(x + 7)(x-4)}$. Cancel out the common factor $(x - 4)$ (assuming $x
eq4$). The simplified form is $\frac{x + 6}{x+7}$.

Answer:

$\frac{x + 6}{x+7}$