Question

find the difference of these rational expressions.

\\\frac{4}{x - 9} - \frac{1}{x + 4}\\

\\\frac{?x + \box}{(x + 4)(x - 9)}\\

Explanation:

Find the least common denominator

Using the Least Common Denominator knowledge point

$$ \text{LCD} = (x - 9)(x + 4) $$

Rewrite each rational expression

Using the Adding Rational Expressions knowledge point

$$ \frac{4}{x - 9} = \frac{4(x + 4)}{(x - 9)(x + 4)} $$

$$ \frac{1}{x + 4} = \frac{1(x - 9)}{(x + 4)(x - 9)} $$

Subtract the numerators

Using the Adding Rational Expressions knowledge point

$$
LATEXBLOCK0
$$

Write the final combined expression

Using the Adding Rational Expressions knowledge point

$$ \frac{3x + 25}{(x + 4)(x - 9)} $$

Answer:

Find the difference of these rational expressions.

$$\frac{4}{x - 9} - \frac{1}{x + 4}$$

The simplified difference is <blank>\(\frac{3x + 25}{(x + 4)(x - 9)}\)</blank>.