Solve 3/2u-v-2u-v/(v-2u)^2

$$\frac { 3 } { 2 u - v } - \frac { 2 u - v } { ( v - 2 u ) ^ { 2 } }$$

Evaluate

$$\frac{2}{2u-v}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2u-v and \left(v-2u\right)^{2} is \left(2u-v\right)^{2}. Multiply \frac{3}{2u-v} times \frac{2u-v}{2u-v}.

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

Since \frac{3\left(2u-v\right)}{\left(2u-v\right)^{2}} and \frac{2u-v}{\left(2u-v\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3\left(2u-v\right)-\left(2u-v\right).

$$\frac{6u-3v-2u+v}{\left(2u-v\right)^{2}}$$

Combine like terms in 6u-3v-2u+v.

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

Factor the expressions that are not already factored in \frac{4u-2v}{\left(2u-v\right)^{2}}.

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

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

$$\frac{2}{2u-v}$$

Expand

$$-\frac{2}{v-2u}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2u-v and \left(v-2u\right)^{2} is \left(2u-v\right)^{2}. Multiply \frac{3}{2u-v} times \frac{2u-v}{2u-v}.

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

Since \frac{3\left(2u-v\right)}{\left(2u-v\right)^{2}} and \frac{2u-v}{\left(2u-v\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3\left(2u-v\right)-\left(2u-v\right).

$$\frac{6u-3v-2u+v}{\left(2u-v\right)^{2}}$$

Combine like terms in 6u-3v-2u+v.

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

Factor the expressions that are not already factored in \frac{4u-2v}{\left(2u-v\right)^{2}}.

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

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

$$\frac{2}{2u-v}$$