Algebra Examples

$\frac{\frac{w + 4}{4} + \frac{1}{2}}{\frac{3}{w} + \frac{1}{2}}$

Step 1

Multiply the numerator and denominator of the fraction by $4 w$ .

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Step 1.1

Multiply $\frac{\frac{w + 4}{4} + \frac{1}{2}}{\frac{3}{w} + \frac{1}{2}}$ by $\frac{4 w}{4 w}$ .

$\frac{4 w}{4 w} \cdot \frac{\frac{w + 4}{4} + \frac{1}{2}}{\frac{3}{w} + \frac{1}{2}}$

Step 1.2

Combine.

$\frac{4 w (\frac{w + 4}{4} + \frac{1}{2})}{4 w (\frac{3}{w} + \frac{1}{2})}$

Step 2

Apply the distributive property.

$\frac{4 w \frac{w + 4}{4} + 4 w \frac{1}{2}}{4 w \frac{3}{w} + 4 w \frac{1}{2}}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $4$ .

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Step 3.1.1

Factor $4$ out of $4 w$ .

$\frac{4 (w) \frac{w + 4}{4} + 4 w \frac{1}{2}}{4 w \frac{3}{w} + 4 w \frac{1}{2}}$

Step 3.1.2

Cancel the common factor.

$\frac{4 w \frac{w + 4}{4} + 4 w \frac{1}{2}}{4 w \frac{3}{w} + 4 w \frac{1}{2}}$

Step 3.1.3

Rewrite the expression.

$\frac{w (w + 4) + 4 w \frac{1}{2}}{4 w \frac{3}{w} + 4 w \frac{1}{2}}$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Factor $2$ out of $4 w$ .

$\frac{w (w + 4) + 2 (2 w) \frac{1}{2}}{4 w \frac{3}{w} + 4 w \frac{1}{2}}$

Step 3.2.2

Cancel the common factor.

$\frac{w (w + 4) + 2 (2 w) \frac{1}{2}}{4 w \frac{3}{w} + 4 w \frac{1}{2}}$

Step 3.2.3

Rewrite the expression.

$\frac{w (w + 4) + 2 w}{4 w \frac{3}{w} + 4 w \frac{1}{2}}$

Step 3.3

Cancel the common factor of $w$ .

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Step 3.3.1

Factor $w$ out of $4 w$ .

$\frac{w (w + 4) + 2 w}{w \cdot 4 \frac{3}{w} + 4 w \frac{1}{2}}$

Step 3.3.2

Cancel the common factor.

$\frac{w (w + 4) + 2 w}{w \cdot 4 \frac{3}{w} + 4 w \frac{1}{2}}$

Step 3.3.3

Rewrite the expression.

$\frac{w (w + 4) + 2 w}{4 \cdot 3 + 4 w \frac{1}{2}}$

Step 3.4

Multiply $4$ by $3$ .

$\frac{w (w + 4) + 2 w}{12 + 4 w \frac{1}{2}}$

Step 3.5

Cancel the common factor of $2$ .

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Step 3.5.1

Factor $2$ out of $4 w$ .

$\frac{w (w + 4) + 2 w}{12 + 2 (2 w) \frac{1}{2}}$

Step 3.5.2

Cancel the common factor.

$\frac{w (w + 4) + 2 w}{12 + 2 (2 w) \frac{1}{2}}$

Step 3.5.3

Rewrite the expression.

$\frac{w (w + 4) + 2 w}{12 + 2 w}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $w$ out of $w (w + 4) + 2 w$ .

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Step 4.1.1

Factor $w$ out of $2 w$ .

$\frac{w (w + 4) + w \cdot 2}{12 + 2 w}$

Step 4.1.2

Factor $w$ out of $w (w + 4) + w \cdot 2$ .

$\frac{w (w + 4 + 2)}{12 + 2 w}$

Step 4.2

Add $4$ and $2$ .

$\frac{w (w + 6)}{12 + 2 w}$

Step 5

Simplify terms.

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Step 5.1

Factor $2$ out of $12 + 2 w$ .

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Step 5.1.1

Factor $2$ out of $12$ .

$\frac{w (w + 6)}{2 \cdot 6 + 2 w}$

Step 5.1.2

Factor $2$ out of $2 \cdot 6 + 2 w$ .

$\frac{w (w + 6)}{2 (6 + w)}$

Step 5.2

Cancel the common factor of $w + 6$ and $6 + w$ .

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Step 5.2.1

Reorder terms.

$\frac{w (w + 6)}{2 (w + 6)}$

Step 5.2.2

Cancel the common factor.

$\frac{w (w + 6)}{2 (w + 6)}$

Step 5.2.3

Rewrite the expression.

$\frac{w}{2}$