Basic Math Examples

$\frac{3}{w} - \frac{18}{w y} + \frac{1}{y}$

Step 1

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

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

Step 2

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

$\frac{3 y}{w y} - \frac{18}{w y} + \frac{1}{y}$

Step 3

Combine the numerators over the common denominator.

$\frac{3 y - 18}{w y} + \frac{1}{y}$

Step 4

Factor $3$ out of $3 y - 18$ .

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Step 4.1

Factor $3$ out of $3 y$ .

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

Step 4.2

Factor $3$ out of $- 18$ .

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

Step 4.3

Factor $3$ out of $3 y + 3 \cdot - 6$ .

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

Step 5

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

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

Step 6

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

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Step 6.1

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

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

Step 6.2

Reorder the factors of $y w$ .

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

Step 7

Combine the numerators over the common denominator.

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

Step 8

Simplify the numerator.

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Step 8.1

Apply the distributive property.

$\frac{3 y + 3 \cdot - 6 + w}{w y}$

Step 8.2

Multiply $3$ by $- 6$ .

$\frac{3 y - 18 + w}{w y}$