Solve 36-p^2/4mpdiv12+2p/6m

$$\frac { 36 - p ^ { 2 } } { 4 m p } \div \frac { 12 + 2 p } { 6 m }$$

Evaluate

$$-\frac{3}{4}+\frac{9}{2p}$$

Short Solution Steps

Divide \frac{36-p^{2}}{4mp} by \frac{12+2p}{6m} by multiplying \frac{36-p^{2}}{4mp} by the reciprocal of \frac{12+2p}{6m}.

$$\frac{\left(36-p^{2}\right)\times 6m}{4mp\left(12+2p\right)}$$

Cancel out 2m in both numerator and denominator.

$$\frac{3\left(-p^{2}+36\right)}{2p\left(2p+12\right)}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in -6-p.

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

Cancel out p+6 in both numerator and denominator.

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

Expand the expression.

$$\frac{-3p+18}{4p}$$

Expand

$$-\frac{3}{4}+\frac{9}{2p}$$

Short Solution Steps

Divide \frac{36-p^{2}}{4mp} by \frac{12+2p}{6m} by multiplying \frac{36-p^{2}}{4mp} by the reciprocal of \frac{12+2p}{6m}.

$$\frac{\left(36-p^{2}\right)\times 6m}{4mp\left(12+2p\right)}$$

Cancel out 2m in both numerator and denominator.

$$\frac{3\left(-p^{2}+36\right)}{2p\left(2p+12\right)}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in -6-p.

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

Cancel out p+6 in both numerator and denominator.

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

Expand the expression.

$$\frac{-3p+18}{4p}$$