Question

question #9 simplify the rational expression $\frac{5x^{2}-8x + 3}{x^{2}+7x - 8}$
$\frac{5x + 3}{x - 8}$
$\frac{5x + 3}{x + 8}$
$\frac{5x - 3}{x - 8}$
$\frac{5x - 3}{x + 8}$

Explanation:

Step1: Factor the numerator

Factor $5x^{2}-8x + 3$. We need two numbers that multiply to $5\times3 = 15$ and add up to $-8$. The numbers are $-5$ and $-3$. So, $5x^{2}-8x + 3=5x^{2}-5x-3x + 3=5x(x - 1)-3(x - 1)=(5x - 3)(x - 1)$.

Step2: Factor the denominator

Factor $x^{2}+7x - 8$. We need two numbers that multiply to $-8$ and add up to $7$. The numbers are $8$ and $-1$. So, $x^{2}+7x - 8=(x + 8)(x - 1)$.

Step3: Simplify the rational - expression

$\frac{5x^{2}-8x + 3}{x^{2}+7x - 8}=\frac{(5x - 3)(x - 1)}{(x + 8)(x - 1)}$. Cancel out the common factor $(x - 1)$ (assuming $x
eq1$). The simplified expression is $\frac{5x - 3}{x + 8}$.

Answer:

$\frac{5x - 3}{x + 8}$