Question

question #9 divide the rational expressions. write the quotient in simplest form. $\frac{x - 9}{2x - 18}div\frac{3}{x - 7}$ $\frac{6}{x - 7}$ $\frac{3(x - 7)}{2}$ $\frac{3}{2(x - 7)}$ $\frac{x - 7}{6}$

Explanation:

Step1: Rewrite division as multiplication

Dividing by a fraction is multiplying by its reciprocal. So, $\frac{x - 9}{2x - 18}\div\frac{3}{x - 7}=\frac{x - 9}{2x - 18}\times\frac{x - 7}{3}$.

Step2: Factor the denominator

Factor out 2 from $2x - 18$, we get $2x-18 = 2(x - 9)$. Then the expression becomes $\frac{x - 9}{2(x - 9)}\times\frac{x - 7}{3}$.

Step3: Simplify the fraction

Cancel out the common factor $(x - 9)$ in $\frac{x - 9}{2(x - 9)}$. We are left with $\frac{1}{2}\times\frac{x - 7}{3}$.

Step4: Multiply the fractions

Multiply the numerators and denominators: $\frac{1\times(x - 7)}{2\times3}=\frac{x - 7}{6}$.

Answer:

$\frac{x - 7}{6}$