Solve 5v/2-v-3/2v^2-6v

$$\frac { 5 v } { 2 } - \frac { v - 3 } { 2 v ^ { 2 } - 6 v }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{v-3}{2v^{2}-6v}.

$$\frac{5v}{2}-\frac{v-3}{2v\left(v-3\right)}$$

Cancel out v-3 in both numerator and denominator.

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

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

$$\frac{5vv}{2v}-\frac{1}{2v}$$

Since \frac{5vv}{2v} and \frac{1}{2v} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5vv-1}{2v}$$

Do the multiplications in 5vv-1.

$$\frac{5v^{2}-1}{2v}$$

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{v-3}{2v^{2}-6v}.

$$\frac{5v}{2}-\frac{v-3}{2v\left(v-3\right)}$$

Cancel out v-3 in both numerator and denominator.

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

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

$$\frac{5vv}{2v}-\frac{1}{2v}$$

Since \frac{5vv}{2v} and \frac{1}{2v} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5vv-1}{2v}$$

Do the multiplications in 5vv-1.

$$\frac{5v^{2}-1}{2v}$$