Simplify 1/(x^3)+1

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

Combine into one fraction.

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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

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

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 $b = x$ .

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

Simplify.

One to any power is one.

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

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

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

Simplify 1/(x^3)+1

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