Solve 1/u-2/v/frac{5{u}-1/v^2}

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of u and v is uv. Multiply \frac{1}{u} times \frac{v}{v}. Multiply \frac{2}{v} times \frac{u}{u}.

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of u and v^{2} is uv^{2}. Multiply \frac{5}{u} times \frac{v^{2}}{v^{2}}. Multiply \frac{1}{v^{2}} times \frac{u}{u}.

$$\frac{\frac{v-2u}{uv}}{\frac{5v^{2}}{uv^{2}}-\frac{u}{uv^{2}}}$$

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

$$\frac{\frac{v-2u}{uv}}{\frac{5v^{2}-u}{uv^{2}}}$$

Divide \frac{v-2u}{uv} by \frac{5v^{2}-u}{uv^{2}} by multiplying \frac{v-2u}{uv} by the reciprocal of \frac{5v^{2}-u}{uv^{2}}.

$$\frac{\left(v-2u\right)uv^{2}}{uv\left(5v^{2}-u\right)}$$

Cancel out uv in both numerator and denominator.

$$\frac{v\left(-2u+v\right)}{-u+5v^{2}}$$

Use the distributive property to multiply v by -2u+v.

$$\frac{-2vu+v^{2}}{-u+5v^{2}}$$

Expand

$$\frac{v^{2}-2uv}{5v^{2}-u}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of u and v is uv. Multiply \frac{1}{u} times \frac{v}{v}. Multiply \frac{2}{v} times \frac{u}{u}.

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of u and v^{2} is uv^{2}. Multiply \frac{5}{u} times \frac{v^{2}}{v^{2}}. Multiply \frac{1}{v^{2}} times \frac{u}{u}.

$$\frac{\frac{v-2u}{uv}}{\frac{5v^{2}}{uv^{2}}-\frac{u}{uv^{2}}}$$

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

$$\frac{\frac{v-2u}{uv}}{\frac{5v^{2}-u}{uv^{2}}}$$

Divide \frac{v-2u}{uv} by \frac{5v^{2}-u}{uv^{2}} by multiplying \frac{v-2u}{uv} by the reciprocal of \frac{5v^{2}-u}{uv^{2}}.

$$\frac{\left(v-2u\right)uv^{2}}{uv\left(5v^{2}-u\right)}$$

Cancel out uv in both numerator and denominator.

$$\frac{v\left(-2u+v\right)}{-u+5v^{2}}$$

Use the distributive property to multiply v by -2u+v.

$$\frac{-2vu+v^{2}}{-u+5v^{2}}$$