Simplify (1-4/(x^2))/(2+4/x)

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

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

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

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

Combine.

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

Apply the distributive property.

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

Simplify by cancelling.

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

Move the leading negative in $- \frac{4}{x^{2}}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the numerator.

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

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

Rewrite $4$ as $2^{2}$ .

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

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 $b = 2$ .

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

Simplify.

Multiply $x$ by $1$ .

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

Multiply $x$ by $1$ .

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

Simplify terms.

Factor $x \cdot 2$ out of $x^{2} \cdot 2 + x \cdot 4$ .

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

$\frac{(x + 2) (x - 2)}{x \cdot 2 (x) + x \cdot 4}$

Factor $x \cdot 2$ out of $x \cdot 4$ .

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

Factor $x \cdot 2$ out of $x \cdot 2 x + x \cdot 2 \cdot 2$ .

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

Cancel the common factor of $x + 2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{x - 2}{x \cdot 2}$

Move $2$ to the left of $x$ .

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

Simplify (1-4/(x^2))/(2+4/x)

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