Algebra Examples

$\frac{1}{2} x^{2} + x + \frac{1}{2} + 2 x + \frac{1}{2} x^{2}$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{1}{2}$ and $x^{2}$ .

$\frac{x^{2}}{2} + x + \frac{1}{2} + 2 x + \frac{1}{2} x^{2}$

Step 1.2

Combine $\frac{1}{2}$ and $x^{2}$ .

$\frac{x^{2}}{2} + x + \frac{1}{2} + 2 x + \frac{x^{2}}{2}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$x + 2 x + \frac{x^{2} + 1 + x^{2}}{2}$

Step 2.2

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

$x + 2 x + \frac{2 x^{2} + 1}{2}$

Step 3

Find the common denominator.

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Step 3.1

Write $x$ as a fraction with denominator $1$ .

$\frac{x}{1} + 2 x + \frac{2 x^{2} + 1}{2}$

Step 3.2

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

$\frac{x}{1} \cdot \frac{2}{2} + 2 x + \frac{2 x^{2} + 1}{2}$

Step 3.3

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

$\frac{x \cdot 2}{2} + 2 x + \frac{2 x^{2} + 1}{2}$

Step 3.4

Write $2 x$ as a fraction with denominator $1$ .

$\frac{x \cdot 2}{2} + \frac{2 x}{1} + \frac{2 x^{2} + 1}{2}$

Step 3.5

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

$\frac{x \cdot 2}{2} + \frac{2 x}{1} \cdot \frac{2}{2} + \frac{2 x^{2} + 1}{2}$

Step 3.6

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

$\frac{x \cdot 2}{2} + \frac{2 x \cdot 2}{2} + \frac{2 x^{2} + 1}{2}$

Step 4

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + 2 x \cdot 2 + 2 x^{2} + 1}{2}$

Step 5

Simplify each term.

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Step 5.1

Move $2$ to the left of $x$ .

$\frac{2 \cdot x + 2 x \cdot 2 + 2 x^{2} + 1}{2}$

Step 5.2

Multiply $2$ by $2$ .

$\frac{2 x + 4 x + 2 x^{2} + 1}{2}$

Step 6

Simplify by adding terms.

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Step 6.1

Add $2 x$ and $4 x$ .

$\frac{6 x + 2 x^{2} + 1}{2}$

Step 6.2

Reorder $6 x$ and $2 x^{2}$ .

$\frac{2 x^{2} + 6 x + 1}{2}$