Solve 1/R=1/R_{1}+1/R_{2}

$$\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } }$$

Solve for R

$$R=\frac{R_{1}R_{2}}{R_{1}+R_{2}}$$

$$R_{2}\neq 0\text{ and }R_{1}\neq 0\text{ and }R_{1}\neq -R_{2}$$

Steps for Solving Linear Equation

Variable R cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by RR_{1}R_{2}, the least common multiple of R,R_{1},R_{2}.

$$R_{1}R_{2}=RR_{2}+RR_{1}$$

Swap sides so that all variable terms are on the left hand side.

$$RR_{2}+RR_{1}=R_{1}R_{2}$$

Combine all terms containing R.

$$\left(R_{2}+R_{1}\right)R=R_{1}R_{2}$$

The equation is in standard form.

$$\left(R_{1}+R_{2}\right)R=R_{1}R_{2}$$

Divide both sides by R_{1}+R_{2}.

$$\frac{\left(R_{1}+R_{2}\right)R}{R_{1}+R_{2}}=\frac{R_{1}R_{2}}{R_{1}+R_{2}}$$

Dividing by R_{1}+R_{2} undoes the multiplication by R_{1}+R_{2}.

$$R=\frac{R_{1}R_{2}}{R_{1}+R_{2}}$$

Variable R cannot be equal to 0.

$$R=\frac{R_{1}R_{2}}{R_{1}+R_{2}}\text{, }R\neq 0$$

Solve for R_1

$$R_{1}=-\frac{RR_{2}}{R-R_{2}}$$

$$R_{2}\neq 0\text{ and }R\neq 0\text{ and }R\neq R_{2}$$

Steps for Solving Linear Equation

Variable R_{1} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by RR_{1}R_{2}, the least common multiple of R,R_{1},R_{2}.

$$R_{1}R_{2}=RR_{2}+RR_{1}$$

Subtract RR_{1} from both sides.

$$R_{1}R_{2}-RR_{1}=RR_{2}$$

Combine all terms containing R_{1}.

$$\left(R_{2}-R\right)R_{1}=RR_{2}$$

Divide both sides by R_{2}-R.

$$\frac{\left(R_{2}-R\right)R_{1}}{R_{2}-R}=\frac{RR_{2}}{R_{2}-R}$$

Dividing by R_{2}-R undoes the multiplication by R_{2}-R.

$$R_{1}=\frac{RR_{2}}{R_{2}-R}$$

Variable R_{1} cannot be equal to 0.

$$R_{1}=\frac{RR_{2}}{R_{2}-R}\text{, }R_{1}\neq 0$$