Finite Math Examples

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

Step 1

To write $\frac{3}{x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2

Write each expression with a common denominator of $2 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

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

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

Step 2.2

Reorder the factors of $x \cdot 2$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

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Step 4.1

Multiply $3$ by $2$ .

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

Step 4.2

Add $1$ and $6$ .

$\frac{7}{2 x} - \frac{1}{3 y}$

Step 5

To write $\frac{7}{2 x}$ as a fraction with a common denominator, multiply by $\frac{3 y}{3 y}$ .

$\frac{7}{2 x} \cdot \frac{3 y}{3 y} - \frac{1}{3 y}$

Step 6

To write $- \frac{1}{3 y}$ as a fraction with a common denominator, multiply by $\frac{2 x}{2 x}$ .

$\frac{7}{2 x} \cdot \frac{3 y}{3 y} - \frac{1}{3 y} \cdot \frac{2 x}{2 x}$

Step 7

Write each expression with a common denominator of $6 x y$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{7}{2 x}$ by $\frac{3 y}{3 y}$ .

$\frac{7 (3 y)}{2 x (3 y)} - \frac{1}{3 y} \cdot \frac{2 x}{2 x}$

Step 7.2

Multiply $3$ by $2$ .

$\frac{7 (3 y)}{6 x y} - \frac{1}{3 y} \cdot \frac{2 x}{2 x}$

Step 7.3

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

$\frac{7 (3 y)}{6 x y} - \frac{2 x}{3 y (2 x)}$

Step 7.4

Multiply $2$ by $3$ .

$\frac{7 (3 y)}{6 x y} - \frac{2 x}{6 y x}$

Step 7.5

Reorder the factors of $6 y x$ .

$\frac{7 (3 y)}{6 x y} - \frac{2 x}{6 x y}$

Step 8

Combine the numerators over the common denominator.

$\frac{7 (3 y) - 2 x}{6 x y}$

Step 9

Multiply $7$ by $3$ .

$\frac{21 y - 2 x}{6 x y}$