Solve 2/1/p+1/r

$$\frac { 2 } { 1 / p + 1 / r }$$

Evaluate

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

Solution Steps

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

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

Since \frac{r}{pr} and \frac{p}{pr} have the same denominator, add them by adding their numerators.

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

Divide 2 by \frac{r+p}{pr} by multiplying 2 by the reciprocal of \frac{r+p}{pr}.

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

Differentiate w.r.t. r

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