Question

multiply.
\\(\frac{3x - 9}{9x^2 - 4} \cdot \frac{3x - 2}{5x + 7}\\)
simplify your answer as much as possible.

Explanation:

Step1: Factor numerator/denominator

Factor $3x-9=3(x-3)$; $9x^2-4=(3x-2)(3x+2)$

Step2: Rewrite the expression

$$\frac{3(x-3)}{(3x-2)(3x+2)} \cdot \frac{3x-2}{5x+7}$$

Step3: Cancel common factors

Cancel $(3x-2)$ from numerator/denominator:
$$\frac{3(x-3)}{3x+2} \cdot \frac{1}{5x+7}$$

Step4: Multiply remaining terms

Multiply numerators and denominators:
$$\frac{3(x-3)}{(3x+2)(5x+7)}$$

Step5: Expand denominator (optional, simplified)

$$\frac{3x-9}{15x^2+21x+10x+14} = \frac{3x-9}{15x^2+31x+14}$$

Answer:

$\frac{3(x-3)}{(3x+2)(5x+7)}$ (or expanded form $\frac{3x-9}{15x^2+31x+14}$)