Solve 4v/v-1/v^2/1-frac{1{2v}}

$$\frac { \frac { 4 v } { v } - \frac { 1 } { v ^ { 2 } } } { 1 - \frac { 1 } { 2 v } }$$

Evaluate

$$4+\frac{2}{v}$$

Short Solution Steps

Cancel out v in both numerator and denominator.

$$\frac{4-\frac{1}{v^{2}}}{1-\frac{1}{2v}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{v^{2}}{v^{2}}.

$$\frac{\frac{4v^{2}}{v^{2}}-\frac{1}{v^{2}}}{1-\frac{1}{2v}}$$

Since \frac{4v^{2}}{v^{2}} and \frac{1}{v^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4v^{2}-1}{v^{2}}}{1-\frac{1}{2v}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2v}{2v}.

$$\frac{\frac{4v^{2}-1}{v^{2}}}{\frac{2v}{2v}-\frac{1}{2v}}$$

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

$$\frac{\frac{4v^{2}-1}{v^{2}}}{\frac{2v-1}{2v}}$$

Divide \frac{4v^{2}-1}{v^{2}} by \frac{2v-1}{2v} by multiplying \frac{4v^{2}-1}{v^{2}} by the reciprocal of \frac{2v-1}{2v}.

$$\frac{\left(4v^{2}-1\right)\times 2v}{v^{2}\left(2v-1\right)}$$

Cancel out v in both numerator and denominator.

$$\frac{2\left(4v^{2}-1\right)}{v\left(2v-1\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 2v-1 in both numerator and denominator.

$$\frac{2\left(2v+1\right)}{v}$$

Expand the expression.

$$\frac{4v+2}{v}$$

Expand

$$4+\frac{2}{v}$$

Short Solution Steps

Cancel out v in both numerator and denominator.

$$\frac{4-\frac{1}{v^{2}}}{1-\frac{1}{2v}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{v^{2}}{v^{2}}.

$$\frac{\frac{4v^{2}}{v^{2}}-\frac{1}{v^{2}}}{1-\frac{1}{2v}}$$

Since \frac{4v^{2}}{v^{2}} and \frac{1}{v^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4v^{2}-1}{v^{2}}}{1-\frac{1}{2v}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2v}{2v}.

$$\frac{\frac{4v^{2}-1}{v^{2}}}{\frac{2v}{2v}-\frac{1}{2v}}$$

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

$$\frac{\frac{4v^{2}-1}{v^{2}}}{\frac{2v-1}{2v}}$$

Divide \frac{4v^{2}-1}{v^{2}} by \frac{2v-1}{2v} by multiplying \frac{4v^{2}-1}{v^{2}} by the reciprocal of \frac{2v-1}{2v}.

$$\frac{\left(4v^{2}-1\right)\times 2v}{v^{2}\left(2v-1\right)}$$

Cancel out v in both numerator and denominator.

$$\frac{2\left(4v^{2}-1\right)}{v\left(2v-1\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 2v-1 in both numerator and denominator.

$$\frac{2\left(2v+1\right)}{v}$$

Expand the expression.

$$\frac{4v+2}{v}$$