Question

simplify.
\frac{\frac{1}{5w} - 3}{\frac{1}{5w} + 7}

Explanation:

Step1: Combine numerator terms

Find common denominator for numerator:
$\frac{1}{5w} - 3 = \frac{1 - 15w}{5w}$

Step2: Combine denominator terms

Find common denominator for denominator:
$\frac{1}{5w} + 7 = \frac{1 + 35w}{5w}$

Step3: Rewrite as fraction division

Replace numerator/denominator with combined forms:
$\frac{\frac{1 - 15w}{5w}}{\frac{1 + 35w}{5w}}$

Step4: Divide by multiplying reciprocal

Cancel $5w$ terms:
$\frac{1 - 15w}{5w} \times \frac{5w}{1 + 35w} = \frac{1 - 15w}{1 + 35w}$

Answer:

$\frac{1 - 15w}{1 + 35w}$