Algebra Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

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

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

Reorder the factors of $y x$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Cancel the common factor of $x y$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

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

Step 7

Apply the distributive property.

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

Step 8

Combine $y$ and $\frac{1}{2}$ .

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

Step 9

Multiply $3 x \frac{1}{2}$ .

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Step 9.1

Combine $3$ and $\frac{1}{2}$ .

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

Step 9.2

Combine $x$ and $\frac{3}{2}$ .

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

Step 10

Combine the numerators over the common denominator.

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

Step 11

Reorder factors in $y + x \cdot 3$ .

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