Question

select the correct answer. which expression is equivalent to \\(\frac{2d - 6}{d^2 + 2d - 48} div \frac{d - 3}{2d + 16}\\) if no denominator equals zero? \\(\bigcirc\\) a. \\(\frac{d - 3}{d - 6}\\) \\(\bigcirc\\) b. \\(\frac{4}{d - 6}\\) \\(\bigcirc\\) c. \\(\frac{4}{d + 8}\\) \\(\bigcirc\\) d. \\(\frac{2(d + 8)}{d - 3}\\)

Explanation:

Step1: Rewrite division as multiplication

$\frac{2d - 6}{d^2 + 2d - 48} \times \frac{2d + 16}{d - 3}$

Step2: Factor all polynomials

$\frac{2(d - 3)}{(d + 8)(d - 6)} \times \frac{2(d + 8)}{d - 3}$

Step3: Cancel common factors

$\frac{2 \times 2}{d - 6}$

Step4: Simplify the numerator

$\frac{4}{d - 6}$

Answer:

B. $\frac{4}{d - 6}$