Solve z^2/z+2+2z/z+2

$$\frac { z ^ { 2 } } { z + 2 } + \frac { 2 z } { z + 2 }$$

Evaluate

$$z$$

Short Solution Steps

Since \frac{z^{2}}{z+2} and \frac{2z}{z+2} have the same denominator, add them by adding their numerators.

$$\frac{z^{2}+2z}{z+2}$$

Factor the expressions that are not already factored in \frac{z^{2}+2z}{z+2}.

$$\frac{z\left(z+2\right)}{z+2}$$

Cancel out z+2 in both numerator and denominator.

$$z$$

Differentiate w.r.t. z

$$1$$

Steps Using Definition of a Derivative

Since \frac{z^{2}}{z+2} and \frac{2z}{z+2} have the same denominator, add them by adding their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{z^{2}+2z}{z+2})$$

Factor the expressions that are not already factored in \frac{z^{2}+2z}{z+2}.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{z\left(z+2\right)}{z+2})$$

Cancel out z+2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}z}(z)$$

The derivative of ax^{n} is nax^{n-1}.

$$z^{1-1}$$

Subtract 1 from 1.

$$z^{0}$$

For any term t except 0, t^{0}=1.

$$1$$