Algebra Examples

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

Step 1

Remove parentheses.

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

Step 2

Simplify $\frac{1}{\frac{1}{R_{1}} + \frac{1}{R_{2}}}$ .

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Step 2.1

Simplify the denominator.

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Step 2.1.1

To write $\frac{1}{R_{1}}$ as a fraction with a common denominator, multiply by $\frac{R_{2}}{R_{2}}$ .

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

Step 2.1.2

To write $\frac{1}{R_{2}}$ as a fraction with a common denominator, multiply by $\frac{R_{1}}{R_{1}}$ .

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

Step 2.1.3

Write each expression with a common denominator of $R_{1} R_{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1.3.1

Multiply $\frac{1}{R_{1}}$ by $\frac{R_{2}}{R_{2}}$ .

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

Step 2.1.3.2

Multiply $\frac{1}{R_{2}}$ by $\frac{R_{1}}{R_{1}}$ .

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

Step 2.1.3.3

Reorder the factors of $R_{2} R_{1}$ .

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

Step 2.1.4

Combine the numerators over the common denominator.

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

Step 2.2

Multiply the numerator by the reciprocal of the denominator.

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

Step 2.3

Multiply $\frac{R_{1} R_{2}}{R_{2} + R_{1}}$ by $1$ .

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