Trigonometry Examples

$\frac{1}{\frac{1}{a} + \frac{1}{b}}$

Step 1

Simplify the denominator.

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Step 1.1

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

$\frac{1}{\frac{1}{a} \cdot \frac{b}{b} + \frac{1}{b}}$

Step 1.2

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

$\frac{1}{\frac{1}{a} \cdot \frac{b}{b} + \frac{1}{b} \cdot \frac{a}{a}}$

Step 1.3

Write each expression with a common denominator of $a b$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{1}{a}$ by $\frac{b}{b}$ .

$\frac{1}{\frac{b}{a b} + \frac{1}{b} \cdot \frac{a}{a}}$

Step 1.3.2

Multiply $\frac{1}{b}$ by $\frac{a}{a}$ .

$\frac{1}{\frac{b}{a b} + \frac{a}{b a}}$

Step 1.3.3

Reorder the factors of $b a$ .

$\frac{1}{\frac{b}{a b} + \frac{a}{a b}}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{1}{\frac{b + a}{a b}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{a b}{b + a}$

Step 3

Multiply $\frac{a b}{b + a}$ by $1$ .

$\frac{a b}{b + a}$