Solve frac{10p^{3}+5p^2-15p}{p^2+5p-6}div4p^2-10p-24/p^2+2p-24

$$\frac { 10 p ^ { 3 } + 5 p ^ { 2 } - 15 p } { p ^ { 2 } + 5 p - 6 } \div \frac { 4 p ^ { 2 } - 10 p - 24 } { p ^ { 2 } + 2 p - 24 }$$

Evaluate

$$\frac{5p}{2}$$

Short Solution Steps

Divide \frac{10p^{3}+5p^{2}-15p}{p^{2}+5p-6} by \frac{4p^{2}-10p-24}{p^{2}+2p-24} by multiplying \frac{10p^{3}+5p^{2}-15p}{p^{2}+5p-6} by the reciprocal of \frac{4p^{2}-10p-24}{p^{2}+2p-24}.

$$\frac{\left(10p^{3}+5p^{2}-15p\right)\left(p^{2}+2p-24\right)}{\left(p^{2}+5p-6\right)\left(4p^{2}-10p-24\right)}$$

Factor the expressions that are not already factored.

$$\frac{5p\left(p-4\right)\left(p-1\right)\left(p+6\right)\left(2p+3\right)}{2\left(p-4\right)\left(p-1\right)\left(p+6\right)\left(2p+3\right)}$$

Cancel out \left(p-4\right)\left(p-1\right)\left(p+6\right)\left(2p+3\right) in both numerator and denominator.

$$\frac{5p}{2}$$

Expand

$$\frac{5p}{2}$$

Short Solution Steps

Divide \frac{10p^{3}+5p^{2}-15p}{p^{2}+5p-6} by \frac{4p^{2}-10p-24}{p^{2}+2p-24} by multiplying \frac{10p^{3}+5p^{2}-15p}{p^{2}+5p-6} by the reciprocal of \frac{4p^{2}-10p-24}{p^{2}+2p-24}.

$$\frac{\left(10p^{3}+5p^{2}-15p\right)\left(p^{2}+2p-24\right)}{\left(p^{2}+5p-6\right)\left(4p^{2}-10p-24\right)}$$

Factor the expressions that are not already factored.

$$\frac{5p\left(p-4\right)\left(p-1\right)\left(p+6\right)\left(2p+3\right)}{2\left(p-4\right)\left(p-1\right)\left(p+6\right)\left(2p+3\right)}$$

Cancel out \left(p-4\right)\left(p-1\right)\left(p+6\right)\left(2p+3\right) in both numerator and denominator.

$$\frac{5p}{2}$$