Pre-Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $3$ .

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Step 1.1.1

Cancel the common factor.

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

Step 1.1.2

Rewrite the expression.

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

Step 1.2

Cancel the common factor of $2$ and $6$ .

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Step 1.2.1

Factor $2$ out of $2 y$ .

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

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $2$ out of $6 x$ .

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

Step 1.2.2.2

Cancel the common factor.

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

Step 1.2.2.3

Rewrite the expression.

$\frac{1}{x y} + \frac{y}{3 x}$

Step 2

To write $\frac{1}{x y}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3

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

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

Step 4

Write each expression with a common denominator of $x y \cdot 3$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{x y}$ by $\frac{3}{3}$ .

$\frac{3}{x y \cdot 3} + \frac{y}{3 x} \cdot \frac{y}{y}$

Step 4.2

Multiply $\frac{y}{3 x}$ by $\frac{y}{y}$ .

$\frac{3}{x y \cdot 3} + \frac{y \cdot y}{3 x y}$

Step 4.3

Reorder the factors of $x y \cdot 3$ .

$\frac{3}{3 x y} + \frac{y \cdot y}{3 x y}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 + y \cdot y}{3 x y}$

Step 6

Multiply $y$ by $y$ .

$\frac{3 + y^{2}}{3 x y}$