Problem 41 - Introductory Algebra for College Students

Question

Divide as indicated. $$\frac{7}{x-5} \div \frac{28}{3 x-15}$$

Step-by-Step Solution

Answer

\(\frac{3}{4}\)

Step 1: Rewrite the division as a multiplication

Rewrite \(\frac{7}{x-5} \div \frac{28}{3x-15}\) as \(\frac{7}{x-5} \times \frac{3x-15}{28}\)

Step 2: Simplify

Simplify \(\frac{7}{x-5} \times \frac{3x-15}{28}\) to \(\frac{7}{x-5} \times \frac{3(x-5)}{28}\)

Step 3: Cancel common factors

Cancel out the common factors of \(x-5\) in the numerator and the denominator to get \(\frac{7}{1} \times \frac{3}{28}\)

Step 4: Multiply the fractions

Multiply \(\frac{7}{1} \times \frac{3}{28}\) to get \(\frac{21}{28}\)

Step 5: Simplify the fraction

Simplify the fraction \(\frac{21}{28}\) to \(\frac{3}{4}\) by dividing the numerator and the denominator by their greatest common divisor, 7