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