Calculus Examples

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

Step 1

Combine into one fraction.

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Step 1.1

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

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

Step 1.2

Combine the numerators over the common denominator.

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

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $1$ as $1^{2}$ .

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

Step 2.2

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

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