Simplify ( square root of x-4)/( square root of x+4)

$\frac{\sqrt{x} - 4}{\sqrt{x} + 4}$

Step 1

Multiply $\frac{\sqrt{x} - 4}{\sqrt{x} + 4}$ by $\frac{\sqrt{x} - 4}{\sqrt{x} - 4}$ .

$\frac{\sqrt{x} - 4}{\sqrt{x} + 4} \cdot \frac{\sqrt{x} - 4}{\sqrt{x} - 4}$

Step 2

Combine fractions.

Multiply $\frac{\sqrt{x} - 4}{\sqrt{x} + 4}$ by $\frac{\sqrt{x} - 4}{\sqrt{x} - 4}$ .

$\frac{(\sqrt{x} - 4) (\sqrt{x} - 4)}{(\sqrt{x} + 4) (\sqrt{x} - 4)}$

Expand the denominator using the FOIL method.

$\frac{(\sqrt{x} - 4) (\sqrt{x} - 4)}{{\sqrt{x}}^{2} + \sqrt{x} \cdot - 4 + 4 \sqrt{x} - 16}$

Simplify.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$\frac{(\sqrt{x} - 4) (\sqrt{x} - 4)}{{(x^{\frac{1}{2}})}^{2} - 16}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{(\sqrt{x} - 4) (\sqrt{x} - 4)}{x^{\frac{1}{2} \cdot 2} - 16}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{(\sqrt{x} - 4) (\sqrt{x} - 4)}{x^{\frac{2}{2}} - 16}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{(\sqrt{x} - 4) (\sqrt{x} - 4)}{x^{\frac{2}{2}} - 16}$

Rewrite the expression.

$\frac{(\sqrt{x} - 4) (\sqrt{x} - 4)}{x^{1} - 16}$

Simplify.

$\frac{(\sqrt{x} - 4) (\sqrt{x} - 4)}{x - 16}$

Step 3

Simplify the numerator.

Raise $\sqrt{x} - 4$ to the power of $1$ .

$\frac{{(\sqrt{x} - 4)}^{1} (\sqrt{x} - 4)}{x - 16}$

Raise $\sqrt{x} - 4$ to the power of $1$ .

$\frac{{(\sqrt{x} - 4)}^{1} {(\sqrt{x} - 4)}^{1}}{x - 16}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{{(\sqrt{x} - 4)}^{1 + 1}}{x - 16}$

Add $1$ and $1$ .

$\frac{{(\sqrt{x} - 4)}^{2}}{x - 16}$