Algebra Examples

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

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Factor $x$ out of $x + x^{4}$ .

Tap for more steps...

Step 1.1.1

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

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

Step 1.1.2

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

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

Step 1.1.3

Factor $x$ out of $x^{4}$ .

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

Step 1.1.4

Factor $x$ out of $x \cdot 1 + x \cdot x^{3}$ .

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

Step 1.2

Rewrite $1$ as $1^{3}$ .

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

Step 1.3

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = 1$ and $b = x$ .

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

Step 1.4

Simplify.

Tap for more steps...

Step 1.4.1

One to any power is one.

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

Step 1.4.2

Rewrite $- 1 x$ as $- x$ .

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

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

Step 2

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

Tap for more steps...

Step 2.1

Reorder terms.

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

Step 2.2

Cancel the common factor.

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

Step 2.3

Divide $x (1 + x)$ by $1$ .

$x (1 + x)$

Step 3

Apply the distributive property.

$x \cdot 1 + x \cdot x$

Step 4

Multiply $x$ by $1$ .

$x + x \cdot x$

Step 5

Multiply $x$ by $x$ .

$x + x^{2}$