Question

select the correct answer.

if no denominator equals zero, which expression is equivalent to \frac{15}{x - 6} + \frac{7}{x + 6}?

\bigcirc \frac{22x + 132}{x^2 - 36}
\bigcirc \frac{22x - 48}{x^2 - 36}
\bigcirc \frac{22}{x^2 - 36}
\bigcirc \frac{22x + 48}{x^2 - 36}

Explanation:

Find a common denominator

$$ \text{LCD} = (x - 6)(x + 6) = x^2 - 36 $$

Rewrite each fraction with the common denominator

$$ \frac{15}{x - 6} + \frac{7}{x + 6} = \frac{15(x + 6)}{(x - 6)(x + 6)} + \frac{7(x - 6)}{(x - 6)(x + 6)} $$

Simplify the numerator

$$
LATEXBLOCK0
$$

Answer:

• (A) \(\frac{22x + 132}{x^2 - 36}\)
• (B) \(\frac{22x - 48}{x^2 - 36}\)
• (C) \(\frac{22}{x^2 - 36}\)
• (D) \(\frac{22x + 48}{x^2 - 36}\) (Correct answer)