Simplify ((w+4)/4+1/2)/(3/w+1/2)

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

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

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

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

Combine.

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

Apply the distributive property.

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

Simplify by cancelling.

Cancel the common factor of $4$ .

Factor $4$ out of $4 w$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $4 w$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $w$ .

Factor $w$ out of $4 w$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $4$ by $3$ .

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

Cancel the common factor of $2$ .

Factor $2$ out of $4 w$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the numerator.

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

Factor $w$ out of $2 w$ .

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

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

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

Add $4$ and $2$ .

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

Simplify terms.

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

Factor $2$ out of $12$ .

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

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

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

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

Reorder terms.

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{w}{2}$

Simplify ((w+4)/4+1/2)/(3/w+1/2)

Related Questions

Support LCMGCF.com by disabling your adblocker.