Simplify -7/( square root of x-4)

$\frac{- 7}{\sqrt{x} - 4}$

Step 1

Move the negative in front of the fraction.

$- \frac{7}{\sqrt{x} - 4}$

Step 2

Multiply $\frac{7}{\sqrt{x} - 4}$ by $\frac{\sqrt{x} + 4}{\sqrt{x} + 4}$ .

$- (\frac{7}{\sqrt{x} - 4} \cdot \frac{\sqrt{x} + 4}{\sqrt{x} + 4})$

Step 3

Multiply $\frac{7}{\sqrt{x} - 4}$ by $\frac{\sqrt{x} + 4}{\sqrt{x} + 4}$ .

$- \frac{7 (\sqrt{x} + 4)}{(\sqrt{x} - 4) (\sqrt{x} + 4)}$

Step 4

Expand the denominator using the FOIL method.

$- \frac{7 (\sqrt{x} + 4)}{{\sqrt{x}}^{2} + \sqrt{x} \cdot 4 - 4 \sqrt{x} - 16}$

Step 5

Simplify.

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

$- \frac{7 (\sqrt{x} + 4)}{{(x^{\frac{1}{2}})}^{2} - 16}$

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

$- \frac{7 (\sqrt{x} + 4)}{x^{\frac{1}{2} \cdot 2} - 16}$

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

$- \frac{7 (\sqrt{x} + 4)}{x^{\frac{2}{2}} - 16}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- \frac{7 (\sqrt{x} + 4)}{x^{\frac{2}{2}} - 16}$

Rewrite the expression.

$- \frac{7 (\sqrt{x} + 4)}{x^{1} - 16}$

Simplify.

$- \frac{7 (\sqrt{x} + 4)}{x - 16}$