Solve r+frac{R_{1}R_{1}}{R_{1}+R_{1}}

$$r + \frac { R _ { 1 } R _ { 1 } } { R _ { 1 } + R _ { 1 } }$$

Evaluate

$$\frac{R_{1}}{2}+r$$

Solution Steps

Multiply R_{1} and R_{1} to get R_{1}^{2}.

$$r+\frac{R_{1}^{2}}{R_{1}+R_{1}}$$

Combine R_{1} and R_{1} to get 2R_{1}.

$$r+\frac{R_{1}^{2}}{2R_{1}}$$

Cancel out R_{1} in both numerator and denominator.

$$r+\frac{R_{1}}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply r times \frac{2}{2}.

$$\frac{2r}{2}+\frac{R_{1}}{2}$$

Since \frac{2r}{2} and \frac{R_{1}}{2} have the same denominator, add them by adding their numerators.

$$\frac{2r+R_{1}}{2}$$

Differentiate w.r.t. r

$$1$$