## Related questions with answers

Question

Perform the indicated operation and, if possible, simplify.

$\frac{a}{6 a-9 b}-\frac{b}{4 a-6 b}$

Solution

VerifiedStep 1

1 of 2$\begin{align*} \frac{a}{3(2a-3b)}-\frac{b}{2(2a-3b)}&=\frac{a}{3(2a-3b)}\cdot\frac{2}{2}-\frac{b}{2(2a-3b)}\cdot\frac{3}{3} &&\text{\textcolor{#4257b2}{Factor the common factor out.}}\\ & &&\text{\textcolor{#4257b2}{$LCD=2\cdot3\cdot(2a-3b)=6(2a-3b)$}}\\ &=\frac{2a}{6(2a-3b)}-\frac{3b}{6(2a-3b)} &&\text{\textcolor{#4257b2}{Multiply.}}\\ &=\frac{\cancel{2a-3b}}{6\cancel{(2a-3b)}} &&\text{\textcolor{#4257b2}{Subtract and cancel.}}\\ &=\boxed{\textcolor{#c34632}{\frac{1}{6}}} \end{align*}$

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