Solve mp+p^2/mp-8p-8mdivp^2-mp/m^2-mp

$$\frac { m p + p ^ { 2 } } { m p - 8 p - 8 m } \div \frac { p ^ { 2 } - m p } { m ^ { 2 } - m p }$$

Evaluate

$$-\frac{m\left(m+p\right)}{mp-8m-8p}$$

Short Solution Steps

Divide \frac{mp+p^{2}}{mp-8p-8m} by \frac{p^{2}-mp}{m^{2}-mp} by multiplying \frac{mp+p^{2}}{mp-8p-8m} by the reciprocal of \frac{p^{2}-mp}{m^{2}-mp}.

$$\frac{\left(mp+p^{2}\right)\left(m^{2}-mp\right)}{\left(mp-8p-8m\right)\left(p^{2}-mp\right)}$$

Factor the expressions that are not already factored.

$$\frac{mp\left(m+p\right)\left(m-p\right)}{p\left(-m+p\right)\left(mp-8m-8p\right)}$$

Extract the negative sign in m-p.

$$\frac{-mp\left(m+p\right)\left(-m+p\right)}{p\left(-m+p\right)\left(mp-8m-8p\right)}$$

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

$$\frac{-m\left(m+p\right)}{mp-8m-8p}$$

Expand the expression.

$$\frac{-m^{2}-mp}{mp-8m-8p}$$

Expand

$$-\frac{m^{2}+mp}{mp-8m-8p}$$

Short Solution Steps

Divide \frac{mp+p^{2}}{mp-8p-8m} by \frac{p^{2}-mp}{m^{2}-mp} by multiplying \frac{mp+p^{2}}{mp-8p-8m} by the reciprocal of \frac{p^{2}-mp}{m^{2}-mp}.

$$\frac{\left(mp+p^{2}\right)\left(m^{2}-mp\right)}{\left(mp-8p-8m\right)\left(p^{2}-mp\right)}$$

Factor the expressions that are not already factored.

$$\frac{mp\left(m+p\right)\left(m-p\right)}{p\left(-m+p\right)\left(mp-8m-8p\right)}$$

Extract the negative sign in m-p.

$$\frac{-mp\left(m+p\right)\left(-m+p\right)}{p\left(-m+p\right)\left(mp-8m-8p\right)}$$

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

$$\frac{-m\left(m+p\right)}{mp-8m-8p}$$

Expand the expression.

$$\frac{-m^{2}-mp}{mp-8m-8p}$$