Pre-Algebra Examples

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

Step 1

To write $x^{3}$ as a fraction with a common denominator, multiply by $\frac{x + 1}{x + 1}$ .

$\frac{x}{x + 1} + \frac{x^{3} (x + 1)}{x + 1}$

Step 2

Combine the numerators over the common denominator.

$\frac{x + x^{3} (x + 1)}{x + 1}$

Step 3

Simplify the numerator.

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Step 3.1

Factor $x$ out of $x + x^{3} (x + 1)$ .

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Step 3.1.1

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

$\frac{x^{1} + x^{3} (x + 1)}{x + 1}$

Step 3.1.2

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

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

Step 3.1.3

Factor $x$ out of $x^{3} (x + 1)$ .

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

Step 3.1.4

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

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

Step 3.2

Apply the distributive property.

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

Step 3.3

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 3.3.1

Multiply $x^{2}$ by $x$ .

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Step 3.3.1.1

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

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

Step 3.3.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 3.3.2

Add $2$ and $1$ .

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

Step 3.4

Multiply $x^{2}$ by $1$ .

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

Step 3.5

Reorder terms.

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