Solve 5/7v+2/v-1

$$\frac { 5 } { 7 v } + \frac { 2 } { v - 1 }$$

Evaluate

$$\frac{19v-5}{7v\left(v-1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7v and v-1 is 7v\left(v-1\right). Multiply \frac{5}{7v} times \frac{v-1}{v-1}. Multiply \frac{2}{v-1} times \frac{7v}{7v}.

$$\frac{5\left(v-1\right)}{7v\left(v-1\right)}+\frac{2\times 7v}{7v\left(v-1\right)}$$

Since \frac{5\left(v-1\right)}{7v\left(v-1\right)} and \frac{2\times 7v}{7v\left(v-1\right)} have the same denominator, add them by adding their numerators.

$$\frac{5\left(v-1\right)+2\times 7v}{7v\left(v-1\right)}$$

Do the multiplications in 5\left(v-1\right)+2\times 7v.

$$\frac{5v-5+14v}{7v\left(v-1\right)}$$

Combine like terms in 5v-5+14v.

$$\frac{19v-5}{7v\left(v-1\right)}$$

Expand 7v\left(v-1\right).

$$\frac{19v-5}{7v^{2}-7v}$$

Factor

$$\frac{19v-5}{7v\left(v-1\right)}$$