Solve qh^2/5h-5kdivhk/pk-ph

$$\frac { q h ^ { 2 } } { 5 h - 5 k } \div \frac { h k } { p k - p h }$$

Evaluate

$$-\frac{hpq}{5k}$$

Short Solution Steps

Divide \frac{qh^{2}}{5h-5k} by \frac{hk}{pk-ph} by multiplying \frac{qh^{2}}{5h-5k} by the reciprocal of \frac{hk}{pk-ph}.

$$\frac{qh^{2}\left(pk-ph\right)}{\left(5h-5k\right)hk}$$

Cancel out h in both numerator and denominator.

$$\frac{hq\left(kp-hp\right)}{k\left(5h-5k\right)}$$

Factor the expressions that are not already factored.

$$\frac{hpq\left(k-h\right)}{5k\left(h-k\right)}$$

Extract the negative sign in k-h.

$$\frac{-hpq\left(h-k\right)}{5k\left(h-k\right)}$$

Cancel out h-k in both numerator and denominator.

$$\frac{-hpq}{5k}$$

Cancel out -1 in both numerator and denominator.

$$\frac{hpq}{-5k}$$

Differentiate w.r.t. q

$$-\frac{hp}{5k}$$