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

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of z and z+2 is z\left(z+2\right). Multiply \frac{z+2}{z} times \frac{z+2}{z+2}. Multiply \frac{z}{z+2} times \frac{z}{z}.

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

Since \frac{\left(z+2\right)\left(z+2\right)}{z\left(z+2\right)} and \frac{zz}{z\left(z+2\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(z+2\right)\left(z+2\right)+zz.

$$\frac{z^{2}+2z+2z+4+z^{2}}{z\left(z+2\right)}$$

Combine like terms in z^{2}+2z+2z+4+z^{2}.

$$\frac{2z^{2}+4z+4}{z\left(z+2\right)}$$

Expand z\left(z+2\right).

$$\frac{2z^{2}+4z+4}{z^{2}+2z}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of z and z+2 is z\left(z+2\right). Multiply \frac{z+2}{z} times \frac{z+2}{z+2}. Multiply \frac{z}{z+2} times \frac{z}{z}.

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

Since \frac{\left(z+2\right)\left(z+2\right)}{z\left(z+2\right)} and \frac{zz}{z\left(z+2\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(z+2\right)\left(z+2\right)+zz.

$$\frac{z^{2}+2z+2z+4+z^{2}}{z\left(z+2\right)}$$

Combine like terms in z^{2}+2z+2z+4+z^{2}.

$$\frac{2z^{2}+4z+4}{z\left(z+2\right)}$$

Expand z\left(z+2\right).

$$\frac{2z^{2}+4z+4}{z^{2}+2z}$$