Solve p^2-10p+21/p-7*p^2+p-12/(p-3)^2

$$\frac { p ^ { 2 } - 10 p + 21 } { p - 7 } \times \frac { p ^ { 2 } + p - 12 } { ( p - 3 ) ^ { 2 } }$$

Evaluate

$$p+4$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{p^{2}-10p+21}{p-7}.

$$\frac{\left(p-7\right)\left(p-3\right)}{p-7}\times \frac{p^{2}+p-12}{\left(p-3\right)^{2}}$$

Cancel out p-7 in both numerator and denominator.

$$\left(p-3\right)\times \frac{p^{2}+p-12}{\left(p-3\right)^{2}}$$

Factor the expressions that are not already factored in \frac{p^{2}+p-12}{\left(p-3\right)^{2}}.

$$\left(p-3\right)\times \frac{\left(p-3\right)\left(p+4\right)}{\left(p-3\right)^{2}}$$

Cancel out p-3 in both numerator and denominator.

$$\left(p-3\right)\times \frac{p+4}{p-3}$$

Cancel out p-3 and p-3.

$$p+4$$

Expand

$$p+4$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{p^{2}-10p+21}{p-7}.

$$\frac{\left(p-7\right)\left(p-3\right)}{p-7}\times \frac{p^{2}+p-12}{\left(p-3\right)^{2}}$$

Cancel out p-7 in both numerator and denominator.

$$\left(p-3\right)\times \frac{p^{2}+p-12}{\left(p-3\right)^{2}}$$

Factor the expressions that are not already factored in \frac{p^{2}+p-12}{\left(p-3\right)^{2}}.

$$\left(p-3\right)\times \frac{\left(p-3\right)\left(p+4\right)}{\left(p-3\right)^{2}}$$

Cancel out p-3 in both numerator and denominator.

$$\left(p-3\right)\times \frac{p+4}{p-3}$$

Cancel out p-3 and p-3.

$$p+4$$