Question

divide these fractions and select the simplified answer. \\(dfrac{dfrac{7}{x - 5}}{dfrac{12}{2x - 10}}\\) \\(\text{a. } dfrac{84}{3x - 15}\\) \\(\text{b. } 42\\) \\(\text{c. } dfrac{7}{6}\\) \\(\text{d. } dfrac{7}{12}\\) \\(\text{e. } dfrac{1}{x - 5}\\)

Explanation:

Step1: Rewrite division as multiplication

$$\frac{\frac{7}{x-5}}{\frac{12}{2x-10}} = \frac{7}{x-5} \times \frac{2x-10}{12}$$

Step2: Factor denominator term

$$2x-10 = 2(x-5)$$
Substitute into the expression:
$$\frac{7}{x-5} \times \frac{2(x-5)}{12}$$

Step3: Cancel common factors

Cancel $(x-5)$ from numerator and denominator:
$$7 \times \frac{2}{12}$$

Step4: Simplify the fraction

$$\frac{14}{12} = \frac{7}{6}$$

Answer:

C. $\frac{7}{6}$