Question

current objective
multiply and divide more than two rational expressions

question

simplify the rational expression: \\(\frac{3d + 9}{2d + 2} \cdot \frac{d^2 + 5d + 4}{d^2 - 4} \div \frac{3d - 9}{2d + 4}\\)

provide your answer below:

Explanation:

Convert division to multiplication

Using the Multiplying and Dividing Multiple Rational Expressions knowledge point

$$ \frac{3d+9}{2d+2} \cdot \frac{d^2+5d+4}{d^2-4} \div \frac{3d-9}{2d+4} = \frac{3d+9}{2d+2} \cdot \frac{d^2+5d+4}{d^2-4} \cdot \frac{2d+4}{3d-9} $$

Factor the linear terms

Using the Greatest Common Factor Factoring knowledge point

$$
LATEXBLOCK0
$$

Factor the quadratic terms

Using the Factoring Trinomials and Difference of Squares knowledge points

$$
LATEXBLOCK1
$$

Substitute and simplify the expression

Using the Multiplying and Dividing Multiple Rational Expressions knowledge point

$$
LATEXBLOCK2
$$

Answer:

Simplify the rational expression: <blank>\(\frac{(d+3)(d+4)}{(d-2)(d-3)}\)</blank>