Solve 4p/q-4q/p/frac{2{q}+2/p}

$$\frac { \frac { 4 p } { q } - \frac { 4 q } { p } } { \frac { 2 } { q } + \frac { 2 } { p } }$$

Evaluate

$$2\left(p-q\right)$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of q and p is pq. Multiply \frac{4p}{q} times \frac{p}{p}. Multiply \frac{4q}{p} times \frac{q}{q}.

$$\frac{\frac{4pp}{pq}-\frac{4qq}{pq}}{\frac{2}{q}+\frac{2}{p}}$$

Since \frac{4pp}{pq} and \frac{4qq}{pq} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4pp-4qq}{pq}}{\frac{2}{q}+\frac{2}{p}}$$

Do the multiplications in 4pp-4qq.

$$\frac{\frac{4p^{2}-4q^{2}}{pq}}{\frac{2}{q}+\frac{2}{p}}$$

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

$$\frac{\frac{4p^{2}-4q^{2}}{pq}}{\frac{2p}{pq}+\frac{2q}{pq}}$$

Since \frac{2p}{pq} and \frac{2q}{pq} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4p^{2}-4q^{2}}{pq}}{\frac{2p+2q}{pq}}$$

Divide \frac{4p^{2}-4q^{2}}{pq} by \frac{2p+2q}{pq} by multiplying \frac{4p^{2}-4q^{2}}{pq} by the reciprocal of \frac{2p+2q}{pq}.

$$\frac{\left(4p^{2}-4q^{2}\right)pq}{pq\left(2p+2q\right)}$$

Cancel out pq in both numerator and denominator.

$$\frac{4p^{2}-4q^{2}}{2p+2q}$$

Factor the expressions that are not already factored.

$$\frac{4\left(p+q\right)\left(p-q\right)}{2\left(p+q\right)}$$

Cancel out 2\left(p+q\right) in both numerator and denominator.

$$2\left(p-q\right)$$

Expand the expression.

$$2p-2q$$

Expand

$$2p-2q$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of q and p is pq. Multiply \frac{4p}{q} times \frac{p}{p}. Multiply \frac{4q}{p} times \frac{q}{q}.

$$\frac{\frac{4pp}{pq}-\frac{4qq}{pq}}{\frac{2}{q}+\frac{2}{p}}$$

Since \frac{4pp}{pq} and \frac{4qq}{pq} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4pp-4qq}{pq}}{\frac{2}{q}+\frac{2}{p}}$$

Do the multiplications in 4pp-4qq.

$$\frac{\frac{4p^{2}-4q^{2}}{pq}}{\frac{2}{q}+\frac{2}{p}}$$

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

$$\frac{\frac{4p^{2}-4q^{2}}{pq}}{\frac{2p}{pq}+\frac{2q}{pq}}$$

Since \frac{2p}{pq} and \frac{2q}{pq} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4p^{2}-4q^{2}}{pq}}{\frac{2p+2q}{pq}}$$

Divide \frac{4p^{2}-4q^{2}}{pq} by \frac{2p+2q}{pq} by multiplying \frac{4p^{2}-4q^{2}}{pq} by the reciprocal of \frac{2p+2q}{pq}.

$$\frac{\left(4p^{2}-4q^{2}\right)pq}{pq\left(2p+2q\right)}$$

Cancel out pq in both numerator and denominator.

$$\frac{4p^{2}-4q^{2}}{2p+2q}$$

Factor the expressions that are not already factored.

$$\frac{4\left(p+q\right)\left(p-q\right)}{2\left(p+q\right)}$$

Cancel out 2\left(p+q\right) in both numerator and denominator.

$$2\left(p-q\right)$$

Expand the expression.

$$2p-2q$$