Question

find the sum of these rational expressions.

\\\frac{9}{x - 2} + \frac{1}{x + 7}\\

\\\frac{?x + \quad}{(x - 2)(x + 7)}\\

Explanation:

Find a common denominator

$$ \text{LCD} = (x - 2)(x + 7) $$

Rewrite each fraction with the common denominator

$$ \frac{9}{x - 2} + \frac{1}{x + 7} = \frac{9(x + 7)}{(x - 2)(x + 7)} + \frac{1(x - 2)}{(x - 2)(x + 7)} $$

Combine and simplify the numerators

$$ \frac{9(x + 7) + 1(x - 2)}{(x - 2)(x + 7)} = \frac{9x + 63 + x - 2}{(x - 2)(x + 7)} = \frac{10x + 61}{(x - 2)(x + 7)} $$

Answer:

Find the sum of these rational expressions.

$$\frac{9}{x - 2} + \frac{1}{x + 7}$$

The sum is <blank>\(\frac{10x + 61}{(x - 2)(x + 7)}\)</blank>.