Finite Math Examples

$\frac{3}{a + \frac{1}{\frac{7}{b}}}$

Step 1

Simplify the denominator.

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Step 1.1

To write $a$ as a fraction with a common denominator, multiply by $\frac{\frac{7}{b}}{\frac{7}{b}}$ .

$\frac{3}{\frac{a \frac{7}{b}}{\frac{7}{b}} + \frac{1}{\frac{7}{b}}}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{3}{\frac{a \frac{7}{b} + 1}{\frac{7}{b}}}$

Step 1.3

Rewrite $\frac{a \frac{7}{b} + 1}{\frac{7}{b}}$ in a factored form.

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Step 1.3.1

Combine $a$ and $\frac{7}{b}$ .

$\frac{3}{\frac{\frac{a \cdot 7}{b} + 1}{\frac{7}{b}}}$

Step 1.3.2

Move $7$ to the left of $a$ .

$\frac{3}{\frac{\frac{7 \cdot a}{b} + 1}{\frac{7}{b}}}$

Step 1.3.3

Write $1$ as a fraction with a common denominator.

$\frac{3}{\frac{\frac{7 a}{b} + \frac{b}{b}}{\frac{7}{b}}}$

Step 1.3.4

Combine the numerators over the common denominator.

$\frac{3}{\frac{\frac{7 a + b}{b}}{\frac{7}{b}}}$

Step 1.4

Multiply the numerator by the reciprocal of the denominator.

$\frac{3}{\frac{7 a + b}{b} \cdot \frac{b}{7}}$

Step 1.5

Cancel the common factor of $b$ .

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Step 1.5.1

Cancel the common factor.

$\frac{3}{\frac{7 a + b}{b} \cdot \frac{b}{7}}$

Step 1.5.2

Rewrite the expression.

$\frac{3}{(7 a + b) \frac{1}{7}}$

Step 1.6

Apply the distributive property.

$\frac{3}{7 a \frac{1}{7} + b \frac{1}{7}}$

Step 1.7

Cancel the common factor of $7$ .

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Step 1.7.1

Factor $7$ out of $7 a$ .

$\frac{3}{7 (a) \frac{1}{7} + b \frac{1}{7}}$

Step 1.7.2

Cancel the common factor.

$\frac{3}{7 a \frac{1}{7} + b \frac{1}{7}}$

Step 1.7.3

Rewrite the expression.

$\frac{3}{a + b \frac{1}{7}}$

Step 1.8

Combine $b$ and $\frac{1}{7}$ .

$\frac{3}{a + \frac{b}{7}}$

Step 1.9

To write $a$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{3}{a \cdot \frac{7}{7} + \frac{b}{7}}$

Step 1.10

Combine $a$ and $\frac{7}{7}$ .

$\frac{3}{\frac{a \cdot 7}{7} + \frac{b}{7}}$

Step 1.11

Combine the numerators over the common denominator.

$\frac{3}{\frac{a \cdot 7 + b}{7}}$

Step 1.12

Move $7$ to the left of $a$ .

$\frac{3}{\frac{7 a + b}{7}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$3 \frac{7}{7 a + b}$

Step 3

Multiply $3 \frac{7}{7 a + b}$ .

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Step 3.1

Combine $3$ and $\frac{7}{7 a + b}$ .

$\frac{3 \cdot 7}{7 a + b}$

Step 3.2

Multiply $3$ by $7$ .

$\frac{21}{7 a + b}$