Solve p-r/p+2r/p-r

$$\frac { p - r } { p } + \frac { 2 r } { p - r }$$

Evaluate

$$\frac{p^{2}+r^{2}}{p\left(p-r\right)}$$

Short Solution Steps

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

$$\frac{\left(p-r\right)\left(p-r\right)}{p\left(p-r\right)}+\frac{2rp}{p\left(p-r\right)}$$

Since \frac{\left(p-r\right)\left(p-r\right)}{p\left(p-r\right)} and \frac{2rp}{p\left(p-r\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(p-r\right)\left(p-r\right)+2rp}{p\left(p-r\right)}$$

Do the multiplications in \left(p-r\right)\left(p-r\right)+2rp.

$$\frac{p^{2}-pr-pr+r^{2}+2rp}{p\left(p-r\right)}$$

Combine like terms in p^{2}-pr-pr+r^{2}+2rp.

$$\frac{p^{2}+r^{2}}{p\left(p-r\right)}$$

Expand p\left(p-r\right).

$$\frac{p^{2}+r^{2}}{p^{2}-pr}$$

Expand

$$\frac{p^{2}+r^{2}}{p\left(p-r\right)}$$

Short Solution Steps

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

$$\frac{\left(p-r\right)\left(p-r\right)}{p\left(p-r\right)}+\frac{2rp}{p\left(p-r\right)}$$

Since \frac{\left(p-r\right)\left(p-r\right)}{p\left(p-r\right)} and \frac{2rp}{p\left(p-r\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(p-r\right)\left(p-r\right)+2rp}{p\left(p-r\right)}$$

Do the multiplications in \left(p-r\right)\left(p-r\right)+2rp.

$$\frac{p^{2}-pr-pr+r^{2}+2rp}{p\left(p-r\right)}$$

Combine like terms in p^{2}-pr-pr+r^{2}+2rp.

$$\frac{p^{2}+r^{2}}{p\left(p-r\right)}$$

Expand p\left(p-r\right).

$$\frac{p^{2}+r^{2}}{p^{2}-pr}$$