Question

question #13
divide the rational expressions. write the quotient in simplest form.
$\frac{3}{x - 6}div\frac{x - 3}{7x - 42}$
$\frac{x - 3}{21}$
$\frac{3}{x - 3}$
$21$
$\frac{21}{x - 3}$

Explanation:

Step1: Change division to multiplication

Dividing by a fraction is multiplying by its reciprocal. So $\frac{3}{x - 6}\div\frac{x - 3}{7x - 42}=\frac{3}{x - 6}\times\frac{7x - 42}{x - 3}$.

Step2: Factor the expression

Factor out 7 from $7x - 42$ to get $7(x - 6)$. Then the expression becomes $\frac{3}{x - 6}\times\frac{7(x - 6)}{x - 3}$.

Step3: Cancel out common factors

Cancel out the common factor $(x - 6)$ in the numerator and denominator. We have $\frac{3\times7}{x - 3}=\frac{21}{x - 3}$.

Answer:

$\frac{21}{x - 3}$