Simplify 1/2x^2+x+1/2+2x+1/2x^2

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

Step 1

Simplify each term.

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

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

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.

Combine the numerators over the common denominator.

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

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

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

Step 3

Find the common denominator.

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

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

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

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

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

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

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

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

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

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

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.

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

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

Multiply $2$ by $2$ .

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

Step 6

Simplify by adding terms.

Add $2 x$ and $4 x$ .

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

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

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