Solve V/R_{1+100}+V/R_{1}

$$\frac { V } { R _ { 1 } + 100 } + \frac { V } { R _ { 1 } }$$

Evaluate

$$\frac{2V\left(R_{1}+50\right)}{R_{1}\left(R_{1}+100\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of R_{1}+100 and R_{1} is R_{1}\left(R_{1}+100\right). Multiply \frac{V}{R_{1}+100} times \frac{R_{1}}{R_{1}}. Multiply \frac{V}{R_{1}} times \frac{R_{1}+100}{R_{1}+100}.

$$\frac{VR_{1}}{R_{1}\left(R_{1}+100\right)}+\frac{V\left(R_{1}+100\right)}{R_{1}\left(R_{1}+100\right)}$$

Since \frac{VR_{1}}{R_{1}\left(R_{1}+100\right)} and \frac{V\left(R_{1}+100\right)}{R_{1}\left(R_{1}+100\right)} have the same denominator, add them by adding their numerators.

$$\frac{VR_{1}+V\left(R_{1}+100\right)}{R_{1}\left(R_{1}+100\right)}$$

Do the multiplications in VR_{1}+V\left(R_{1}+100\right).

$$\frac{VR_{1}+VR_{1}+100V}{R_{1}\left(R_{1}+100\right)}$$

Combine like terms in VR_{1}+VR_{1}+100V.

$$\frac{2VR_{1}+100V}{R_{1}\left(R_{1}+100\right)}$$

Expand R_{1}\left(R_{1}+100\right).

$$\frac{2VR_{1}+100V}{R_{1}^{2}+100R_{1}}$$

Factor

$$\frac{2V\left(R_{1}+50\right)}{R_{1}\left(R_{1}+100\right)}$$