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\frac{1}{eg}
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\frac{1}{eg}
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\frac{\left(f-2\right)\left(g+3\right)}{\left(eg+3e\right)\left(fg-2g\right)}
Divide \frac{f-2}{eg+3e} by \frac{fg-2g}{g+3} by multiplying \frac{f-2}{eg+3e} by the reciprocal of \frac{fg-2g}{g+3}.
\frac{\left(f-2\right)\left(g+3\right)}{eg\left(f-2\right)\left(g+3\right)}
Factor the expressions that are not already factored.
\frac{1}{eg}
Cancel out \left(f-2\right)\left(g+3\right) in both numerator and denominator.
\frac{\left(f-2\right)\left(g+3\right)}{\left(eg+3e\right)\left(fg-2g\right)}
Divide \frac{f-2}{eg+3e} by \frac{fg-2g}{g+3} by multiplying \frac{f-2}{eg+3e} by the reciprocal of \frac{fg-2g}{g+3}.
\frac{\left(f-2\right)\left(g+3\right)}{eg\left(f-2\right)\left(g+3\right)}
Factor the expressions that are not already factored.
\frac{1}{eg}
Cancel out \left(f-2\right)\left(g+3\right) in both numerator and denominator.
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