Question

add. simplify, if possible.

\\\frac{6}{x-8} + \frac{23}{(x-8)^2}\\

\\\frac{6}{x-8} + \frac{23}{(x-8)^2} = \quad \text{(simplify your answer.)}\\

Explanation:

Find the least common denominator

Using the Least Common Denominator knowledge point

$$ \text{LCD} = (x-8)^2 $$

Rewrite the first rational expression

Using the Rational Expressions knowledge point

$$ \frac{6}{x-8} = \frac{6(x-8)}{(x-8)^2} = \frac{6x-48}{(x-8)^2} $$

Add the numerators

Combine the numerators over the common denominator:

$$ \frac{6x-48}{(x-8)^2} + \frac{23}{(x-8)^2} = \frac{6x-48+23}{(x-8)^2} $$

Simplify the numerator

Combine the constant terms:

$$ \frac{6x-25}{(x-8)^2} $$

Answer:

\(\frac{6}{x-8} + \frac{23}{(x-8)^2} =\) <blank>\(\frac{6x-25}{(x-8)^2}\)</blank> (Simplify your answer.)