Algebra Examples

$\frac{x^{8} + x^{6}}{x}$

Step 1

Factor $x^{6}$ out of $x^{8} + x^{6}$ .

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Step 1.1

Factor $x^{6}$ out of $x^{8}$ .

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

Step 1.2

Multiply by $1$ .

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

Step 1.3

Factor $x^{6}$ out of $x^{6} x^{2} + x^{6} \cdot 1$ .

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

Step 2

Cancel the common factor of $x^{6}$ and $x$ .

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Step 2.1

Factor $x$ out of $x^{6} (x^{2} + 1)$ .

$\frac{x (x^{5} (x^{2} + 1))}{x}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

$\frac{x (x^{5} (x^{2} + 1))}{x^{1}}$

Step 2.2.2

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

$\frac{x (x^{5} (x^{2} + 1))}{x \cdot 1}$

Step 2.2.3

Cancel the common factor.

$\frac{x (x^{5} (x^{2} + 1))}{x \cdot 1}$

Step 2.2.4

Rewrite the expression.

$\frac{x^{5} (x^{2} + 1)}{1}$

Step 2.2.5

Divide $x^{5} (x^{2} + 1)$ by $1$ .

$x^{5} (x^{2} + 1)$

Step 3

Apply the distributive property.

$x^{5} x^{2} + x^{5} \cdot 1$

Step 4

Multiply $x^{5}$ by $x^{2}$ by adding the exponents.

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Step 4.1

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

$x^{5 + 2} + x^{5} \cdot 1$

Step 4.2

Add $5$ and $2$ .

$x^{7} + x^{5} \cdot 1$

Step 5

Multiply $x^{5}$ by $1$ .

$x^{7} + x^{5}$