Solve p^2-2p-3/p^2-p-6divp^2-1/p^2+2p

$$\frac { p ^ { 2 } - 2 p - 3 } { p ^ { 2 } - p - 6 } \div \frac { p ^ { 2 } - 1 } { p ^ { 2 } + 2 p }$$

Evaluate

$$\frac{p}{p-1}$$

Short Solution Steps

Divide \frac{p^{2}-2p-3}{p^{2}-p-6} by \frac{p^{2}-1}{p^{2}+2p} by multiplying \frac{p^{2}-2p-3}{p^{2}-p-6} by the reciprocal of \frac{p^{2}-1}{p^{2}+2p}.

$$\frac{\left(p^{2}-2p-3\right)\left(p^{2}+2p\right)}{\left(p^{2}-p-6\right)\left(p^{2}-1\right)}$$

Factor the expressions that are not already factored.

$$\frac{p\left(p-3\right)\left(p+1\right)\left(p+2\right)}{\left(p-3\right)\left(p-1\right)\left(p+1\right)\left(p+2\right)}$$

Cancel out \left(p-3\right)\left(p+1\right)\left(p+2\right) in both numerator and denominator.

$$\frac{p}{p-1}$$

Expand

$$\frac{p}{p-1}$$

Short Solution Steps

Divide \frac{p^{2}-2p-3}{p^{2}-p-6} by \frac{p^{2}-1}{p^{2}+2p} by multiplying \frac{p^{2}-2p-3}{p^{2}-p-6} by the reciprocal of \frac{p^{2}-1}{p^{2}+2p}.

$$\frac{\left(p^{2}-2p-3\right)\left(p^{2}+2p\right)}{\left(p^{2}-p-6\right)\left(p^{2}-1\right)}$$

Factor the expressions that are not already factored.

$$\frac{p\left(p-3\right)\left(p+1\right)\left(p+2\right)}{\left(p-3\right)\left(p-1\right)\left(p+1\right)\left(p+2\right)}$$

Cancel out \left(p-3\right)\left(p+1\right)\left(p+2\right) in both numerator and denominator.

$$\frac{p}{p-1}$$