Question

question 5
2 pts
simplify each expression.
\\(\frac{1}{m - 4} \div \frac{m + 2}{5m - 20}\\)
numerator / denominator = \\(\square / \square\\)

Explanation:

Step1: Rewrite division as multiplication

To divide by a fraction, we multiply by its reciprocal. So, $\frac{1}{m - 4} \div \frac{m + 2}{5m - 20}$ becomes $\frac{1}{m - 4} \times \frac{5m - 20}{m + 2}$.

Step2: Factor the numerator

Factor $5m - 20$: $5m - 20 = 5(m - 4)$. Now the expression is $\frac{1}{m - 4} \times \frac{5(m - 4)}{m + 2}$.

Step3: Cancel common factors

The $(m - 4)$ terms in the numerator and denominator cancel out. We are left with $\frac{5}{m + 2}$.

Answer:

Numerator: 5, Denominator: \( m + 2 \) (so the expression is \( \frac{5}{m + 2} \))