Algebra Examples

$\frac{3 + \frac{1}{6 y}}{\frac{y}{2}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(3 + \frac{1}{6 y}) \frac{2}{y}$

Step 2

To write $3$ as a fraction with a common denominator, multiply by $\frac{6 y}{6 y}$ .

$(3 \cdot \frac{6 y}{6 y} + \frac{1}{6 y}) \frac{2}{y}$

Step 3

Combine $3$ and $\frac{6 y}{6 y}$ .

$(\frac{3 (6 y)}{6 y} + \frac{1}{6 y}) \frac{2}{y}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 (6 y) + 1}{6 y} \cdot \frac{2}{y}$

Step 5

Multiply $6$ by $3$ .

$\frac{18 y + 1}{6 y} \cdot \frac{2}{y}$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $6 y$ .

$\frac{18 y + 1}{2 (3 y)} \cdot \frac{2}{y}$

Step 6.2

Cancel the common factor.

$\frac{18 y + 1}{2 (3 y)} \cdot \frac{2}{y}$

Step 6.3

Rewrite the expression.

$\frac{18 y + 1}{3 y} \cdot \frac{1}{y}$

Step 7

Multiply $\frac{18 y + 1}{3 y}$ by $\frac{1}{y}$ .

$\frac{18 y + 1}{3 y \cdot y}$

Step 8

Raise $y$ to the power of $1$ .

$\frac{18 y + 1}{3 (y^{1} y)}$

Step 9

Raise $y$ to the power of $1$ .

$\frac{18 y + 1}{3 (y^{1} y^{1})}$

Step 10

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{18 y + 1}{3 y^{1 + 1}}$

Step 11

Add $1$ and $1$ .

$\frac{18 y + 1}{3 y^{2}}$