Simplify (1-1/(x^2))/(1/x+1/(x^2))

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

Multiply the numerator and denominator of the complex fraction by $x^{2}$ .

Multiply $\frac{1 - \frac{1}{x^{2}}}{\frac{1}{x} + \frac{1}{x^{2}}}$ by $\frac{x^{2}}{x^{2}}$ .

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

Combine.

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

Apply the distributive property.

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

Simplify by cancelling.

Cancel the common factor of $x^{2}$ .

Move the leading negative in $- \frac{1}{x^{2}}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x$ .

Factor $x$ out of $x^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x^{2}$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the numerator.

Rewrite $x^{2} \cdot 1$ as ${(x \cdot 1)}^{2}$ .

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

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

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

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

$\frac{(x \cdot 1 + 1) (x \cdot 1 - 1)}{x + 1}$

Simplify.

Multiply $x$ by $1$ .

$\frac{(x + 1) (x \cdot 1 - 1)}{x + 1}$

Multiply $x$ by $1$ .

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

Cancel the common factor of $x + 1$ .

Cancel the common factor.

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

Divide $x - 1$ by $1$ .

$x - 1$

Simplify (1-1/(x^2))/(1/x+1/(x^2))

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