Question

current objective
simplify a complex rational expression

question
divide: \frac{\frac{4}{x + 3} - \frac{7}{x - 3}}{\frac{6}{x + 3}}.

provide your answer below:

Explanation:

Identify the complex rational expression

Using the Complex Rational Expressions knowledge point

$$ \frac{\frac{4}{x+3} - \frac{7}{x-3}}{\frac{6}{x+3}} $$

Find the LCD of all denominators

Using the Least Common Denominator knowledge point

$$ \text{LCD} = (x+3)(x-3) $$

Simplify the numerator of the complex fraction

Using the Subtracting Rational Expressions knowledge point

$$
LATEXBLOCK0
$$

Divide the simplified numerator by the denominator

Using the Complex Rational Expressions knowledge point

$$
LATEXBLOCK1
$$

Answer:

Divide: \(\frac{\frac{4}{x+3} - \frac{7}{x-3}}{\frac{6}{x+3}}\)

Provide your answer below:
<blank>\(\frac{-x-11}{2x-6}\)</blank>