Solve 9/7v+9/v-6

$$\frac { 9 } { 7 v } + \frac { 9 } { v - 6 }$$

Evaluate

$$\frac{18\left(4v-3\right)}{7v\left(v-6\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7v and v-6 is 7v\left(v-6\right). Multiply \frac{9}{7v} times \frac{v-6}{v-6}. Multiply \frac{9}{v-6} times \frac{7v}{7v}.

$$\frac{9\left(v-6\right)}{7v\left(v-6\right)}+\frac{9\times 7v}{7v\left(v-6\right)}$$

Since \frac{9\left(v-6\right)}{7v\left(v-6\right)} and \frac{9\times 7v}{7v\left(v-6\right)} have the same denominator, add them by adding their numerators.

$$\frac{9\left(v-6\right)+9\times 7v}{7v\left(v-6\right)}$$

Do the multiplications in 9\left(v-6\right)+9\times 7v.

$$\frac{9v-54+63v}{7v\left(v-6\right)}$$

Combine like terms in 9v-54+63v.

$$\frac{72v-54}{7v\left(v-6\right)}$$

Expand 7v\left(v-6\right).

$$\frac{72v-54}{7v^{2}-42v}$$

Factor

$$\frac{18\left(4v-3\right)}{7v\left(v-6\right)}$$