Question

find the product or quotient.
$\frac{5x - 5}{7}div\frac{7x - 7}{3}$
$\frac{5x - 5}{7}div\frac{7x - 7}{3}=square$
(simplify your answer)

Explanation:

Step1: Factor out common factors

Factor 5 from \(5x - 5\) to get \(5(x - 1)\) and 7 from \(7x - 7\) to get \(7(x - 1)\). The expression becomes \(\frac{5(x - 1)}{7}\div\frac{7(x - 1)}{3}\).

Step2: Change division to multiplication

Recall that dividing by a fraction is the same as multiplying by its reciprocal. So \(\frac{5(x - 1)}{7}\div\frac{7(x - 1)}{3}=\frac{5(x - 1)}{7}\times\frac{3}{7(x - 1)}\).

Step3: Cancel out common factors

Cancel out the common factor \((x - 1)\) in the numerator and denominator. We get \(\frac{5}{7}\times\frac{3}{7}\).

Step4: Multiply the fractions

Multiply the numerators together and the denominators together: \(\frac{5\times3}{7\times7}=\frac{15}{49}\).

Answer:

\(\frac{15}{49}\)