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\frac{\left(x^{2}+7x+6\right)\left(2x-3\right)}{\left(x+1\right)\left(x+6\right)}
Divide \frac{x^{2}+7x+6}{x+1} by \frac{x+6}{2x-3} by multiplying \frac{x^{2}+7x+6}{x+1} by the reciprocal of \frac{x+6}{2x-3}.
\frac{\left(2x-3\right)\left(x+1\right)\left(x+6\right)}{\left(x+1\right)\left(x+6\right)}
Factor the expressions that are not already factored.
2x-3
Cancel out \left(x+1\right)\left(x+6\right) in both numerator and denominator.
\frac{\left(x^{2}+7x+6\right)\left(2x-3\right)}{\left(x+1\right)\left(x+6\right)}
Divide \frac{x^{2}+7x+6}{x+1} by \frac{x+6}{2x-3} by multiplying \frac{x^{2}+7x+6}{x+1} by the reciprocal of \frac{x+6}{2x-3}.
\frac{\left(2x-3\right)\left(x+1\right)\left(x+6\right)}{\left(x+1\right)\left(x+6\right)}
Factor the expressions that are not already factored.
2x-3
Cancel out \left(x+1\right)\left(x+6\right) in both numerator and denominator.
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Limits
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