Basic Math Examples

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

Step 1

Simplify the denominator.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Combine the numerators over the common denominator.

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

Step 1.4

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

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

Step 1.5

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

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

Step 1.6

Combine the numerators over the common denominator.

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

Step 1.7

Reorder terms.

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

Step 1.8

Rewrite $\frac{3 \cdot 3 y \cdot y + 3 \cdot 6 y - 2}{3 y}$ in a factored form.

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Step 1.8.1

Multiply $y$ by $y$ by adding the exponents.

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Step 1.8.1.1

Move $y$ .

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

Step 1.8.1.2

Multiply $y$ by $y$ .

$\frac{1}{\frac{3 \cdot 3 y^{2} + 3 \cdot 6 y - 2}{3 y}}$

Step 1.8.2

Multiply $3$ by $3$ .

$\frac{1}{\frac{9 y^{2} + 3 \cdot 6 y - 2}{3 y}}$

Step 1.8.3

Multiply $3$ by $6$ .

$\frac{1}{\frac{9 y^{2} + 18 y - 2}{3 y}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{3 y}{9 y^{2} + 18 y - 2}$

Step 3

Multiply $\frac{3 y}{9 y^{2} + 18 y - 2}$ by $1$ .

$\frac{3 y}{9 y^{2} + 18 y - 2}$