Basic Math Examples

$\frac{w^{2} + 3}{2 w + 2} + \frac{w}{2}$

Step 1

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

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Step 1.1

Factor $2$ out of $2 w$ .

$\frac{w^{2} + 3}{2 (w) + 2} + \frac{w}{2}$

Step 1.2

Factor $2$ out of $2$ .

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

Step 1.3

Factor $2$ out of $2 (w) + 2 (1)$ .

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

Step 2

To write $\frac{w}{2}$ as a fraction with a common denominator, multiply by $\frac{w + 1}{w + 1}$ .

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

Step 3

Simplify terms.

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Step 3.1

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

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

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

Step 4.2

Multiply $w$ by $w$ .

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

Step 4.3

Multiply $w$ by $1$ .

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

Step 4.4

Add $w^{2}$ and $w^{2}$ .

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

Step 4.5

Reorder terms.

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