Solve -h/a^2+ah/h

$$\frac { \frac { - h } { a ^ { 2 } + a h } } { h }$$

Evaluate

$$-\frac{1}{a\left(a+h\right)}$$

Short Solution Steps

Express \frac{\frac{-h}{a^{2}+ah}}{h} as a single fraction.

$$\frac{-h}{\left(a^{2}+ah\right)h}$$

Use the distributive property to multiply a^{2}+ah by h.

$$\frac{-h}{a^{2}h+ah^{2}}$$

Factor the expressions that are not already factored.

$$\frac{-h}{ah\left(a+h\right)}$$

Cancel out h in both numerator and denominator.

$$\frac{-1}{a\left(a+h\right)}$$

Expand the expression.

$$\frac{-1}{a^{2}+ah}$$

Differentiate w.r.t. a

$$\frac{2a+h}{\left(a\left(a+h\right)\right)^{2}}$$