Question

select the correct answer.

which expression is equivalent to this quotient?
\\\frac{6}{28x + 4} \div \frac{12}{35x + 5}\\

• \\(\frac{72}{20(7x + 1)}\\)
• \\(\frac{5}{8}\\)
• \\(\frac{8}{5}\\)
• \\(\frac{7x + 1}{8}\\)

Explanation:

Convert division to multiplication by the reciprocal

$$ \frac{6}{28x + 4} \div \frac{12}{35x + 5} = \frac{6}{28x + 4} \cdot \frac{35x + 5}{12} $$

Factor the denominators and numerators

$$
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Substitute and simplify the expression

$$ \frac{6}{4(7x + 1)} \cdot \frac{5(7x + 1)}{12} = \frac{6 \cdot 5 \cdot (7x + 1)}{4 \cdot 12 \cdot (7x + 1)} = \frac{30}{48} = \frac{5}{8} $$

Answer:

• (A) \(\frac{72}{20(7x + 1)}\)
• (B) \(\frac{5}{8}\) (Correct answer)
• (C) \(\frac{8}{5}\)
• (D) \(\frac{7x + 1}{8}\)