Question

question

simplify the rational expression: \\(\frac{4m + 4}{3m - 15} \cdot \frac{m^2 - 3m - 10}{m^2 - 4m - 32} \div \frac{12m - 36}{6m - 48}

provide your answer below:

Explanation:

Convert division to multiplication

Using the Dividing Rational Expressions knowledge point

$$ \frac{4m + 4}{3m - 15} \cdot \frac{m^2 - 3m - 10}{m^2 - 4m - 32} \div \frac{12m - 36}{6m - 48} = \frac{4m + 4}{3m - 15} \cdot \frac{m^2 - 3m - 10}{m^2 - 4m - 32} \cdot \frac{6m - 48}{12m - 36} $$

Factor all linear terms

Using the Greatest Common Factor Factoring knowledge point

$$
LATEXBLOCK0
$$

Factor all quadratic trinomials

Using the Factoring Trinomials knowledge point

$$
LATEXBLOCK1
$$

Multiply and simplify the expression

Using the Multiplying Rational Expressions and Simplifying Rational Expressions knowledge points

$$
LATEXBLOCK2
$$

Answer:

$$\frac{2(m + 1)(m + 2)}{3(m + 4)(m - 3)}$$