Solve 1/p-7divp+1/p^2-p-42

$$\frac { 1 } { p - 7 } \div \frac { p + 1 } { p ^ { 2 } - p - 42 }$$

Evaluate

$$\frac{p+6}{p+1}$$

Short Solution Steps

Divide \frac{1}{p-7} by \frac{p+1}{p^{2}-p-42} by multiplying \frac{1}{p-7} by the reciprocal of \frac{p+1}{p^{2}-p-42}.

$$\frac{p^{2}-p-42}{\left(p-7\right)\left(p+1\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(p-7\right)\left(p+6\right)}{\left(p-7\right)\left(p+1\right)}$$

Cancel out p-7 in both numerator and denominator.

$$\frac{p+6}{p+1}$$

Expand

$$\frac{p+6}{p+1}$$

Short Solution Steps

Divide \frac{1}{p-7} by \frac{p+1}{p^{2}-p-42} by multiplying \frac{1}{p-7} by the reciprocal of \frac{p+1}{p^{2}-p-42}.

$$\frac{p^{2}-p-42}{\left(p-7\right)\left(p+1\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(p-7\right)\left(p+6\right)}{\left(p-7\right)\left(p+1\right)}$$

Cancel out p-7 in both numerator and denominator.

$$\frac{p+6}{p+1}$$