Solve 9z/z+10+9z/z-6

$$\frac { 9 z } { z + 10 } + \frac { 9 z } { z - 6 }$$

Evaluate

$$\frac{18z\left(z+2\right)}{\left(z-6\right)\left(z+10\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of z+10 and z-6 is \left(z-6\right)\left(z+10\right). Multiply \frac{9z}{z+10} times \frac{z-6}{z-6}. Multiply \frac{9z}{z-6} times \frac{z+10}{z+10}.

$$\frac{9z\left(z-6\right)}{\left(z-6\right)\left(z+10\right)}+\frac{9z\left(z+10\right)}{\left(z-6\right)\left(z+10\right)}$$

Since \frac{9z\left(z-6\right)}{\left(z-6\right)\left(z+10\right)} and \frac{9z\left(z+10\right)}{\left(z-6\right)\left(z+10\right)} have the same denominator, add them by adding their numerators.

$$\frac{9z\left(z-6\right)+9z\left(z+10\right)}{\left(z-6\right)\left(z+10\right)}$$

Do the multiplications in 9z\left(z-6\right)+9z\left(z+10\right).

$$\frac{9z^{2}-54z+9z^{2}+90z}{\left(z-6\right)\left(z+10\right)}$$

Combine like terms in 9z^{2}-54z+9z^{2}+90z.

$$\frac{18z^{2}+36z}{\left(z-6\right)\left(z+10\right)}$$

Expand \left(z-6\right)\left(z+10\right).

$$\frac{18z^{2}+36z}{z^{2}+4z-60}$$

Factor

$$\frac{18z\left(z+2\right)}{\left(z-6\right)\left(z+10\right)}$$