Pre-Algebra Examples

$\frac{x^{3}}{x^{2} + 1} + \frac{x}{x^{2} + 1}$

Step 1

Combine the numerators over the common denominator.

$\frac{x^{3} + x}{x^{2} + 1}$

Step 2

Factor $x$ out of $x^{3} + x$ .

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Step 2.1

Factor $x$ out of $x^{3}$ .

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

Step 2.2

Raise $x$ to the power of $1$ .

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

Step 2.3

Factor $x$ out of $x^{1}$ .

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

Step 2.4

Factor $x$ out of $x \cdot x^{2} + x \cdot 1$ .

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

Step 3

Cancel the common factor of $x^{2} + 1$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Divide $x$ by $1$ .

$x$