Algebra Examples

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

Step 1

Combine into one fraction.

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Step 1.1

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

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

Step 1.2

Combine the numerators over the common denominator.

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

Step 2

Simplify the numerator.

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Step 2.1

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

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

Step 2.2

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 $b = x$ .

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

Step 2.3

Simplify.

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Step 2.3.1

One to any power is one.

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

Step 2.3.2

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

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