Solve 1/w+1/v/frac{1{v}-1/w}=

$$\frac { \frac { 1 } { w } + \frac { 1 } { v } } { \frac { 1 } { v } - \frac { 1 } { w } } =$$

Evaluate

$$\frac{v+w}{w-v}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of w and v is vw. Multiply \frac{1}{w} times \frac{v}{v}. Multiply \frac{1}{v} times \frac{w}{w}.

$$\frac{\frac{v}{vw}+\frac{w}{vw}}{\frac{1}{v}-\frac{1}{w}}$$

Since \frac{v}{vw} and \frac{w}{vw} have the same denominator, add them by adding their numerators.

$$\frac{\frac{v+w}{vw}}{\frac{1}{v}-\frac{1}{w}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of v and w is vw. Multiply \frac{1}{v} times \frac{w}{w}. Multiply \frac{1}{w} times \frac{v}{v}.

$$\frac{\frac{v+w}{vw}}{\frac{w}{vw}-\frac{v}{vw}}$$

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

$$\frac{\frac{v+w}{vw}}{\frac{w-v}{vw}}$$

Divide \frac{v+w}{vw} by \frac{w-v}{vw} by multiplying \frac{v+w}{vw} by the reciprocal of \frac{w-v}{vw}.

$$\frac{\left(v+w\right)vw}{vw\left(w-v\right)}$$

Cancel out vw in both numerator and denominator.

$$\frac{v+w}{-v+w}$$

Expand

$$\frac{v+w}{w-v}$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of w and v is vw. Multiply \frac{1}{w} times \frac{v}{v}. Multiply \frac{1}{v} times \frac{w}{w}.

$$\frac{\frac{v}{vw}+\frac{w}{vw}}{\frac{1}{v}-\frac{1}{w}}$$

Since \frac{v}{vw} and \frac{w}{vw} have the same denominator, add them by adding their numerators.

$$\frac{\frac{v+w}{vw}}{\frac{1}{v}-\frac{1}{w}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of v and w is vw. Multiply \frac{1}{v} times \frac{w}{w}. Multiply \frac{1}{w} times \frac{v}{v}.

$$\frac{\frac{v+w}{vw}}{\frac{w}{vw}-\frac{v}{vw}}$$

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

$$\frac{\frac{v+w}{vw}}{\frac{w-v}{vw}}$$

Divide \frac{v+w}{vw} by \frac{w-v}{vw} by multiplying \frac{v+w}{vw} by the reciprocal of \frac{w-v}{vw}.

$$\frac{\left(v+w\right)vw}{vw\left(w-v\right)}$$

Cancel out vw in both numerator and denominator.

$$\frac{v+w}{-v+w}$$