Simplify -9/( square root of x-2)

$\frac{- 9}{\sqrt{x} - 2}$

Step 1

Move the negative in front of the fraction.

$- \frac{9}{\sqrt{x} - 2}$

Step 2

Multiply $\frac{9}{\sqrt{x} - 2}$ by $\frac{\sqrt{x} + 2}{\sqrt{x} + 2}$ .

$- (\frac{9}{\sqrt{x} - 2} \cdot \frac{\sqrt{x} + 2}{\sqrt{x} + 2})$

Step 3

Multiply $\frac{9}{\sqrt{x} - 2}$ by $\frac{\sqrt{x} + 2}{\sqrt{x} + 2}$ .

$- \frac{9 (\sqrt{x} + 2)}{(\sqrt{x} - 2) (\sqrt{x} + 2)}$

Step 4

Expand the denominator using the FOIL method.

$- \frac{9 (\sqrt{x} + 2)}{{\sqrt{x}}^{2} + \sqrt{x} \cdot 2 - 2 \sqrt{x} - 4}$

Step 5

Simplify.

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

$- \frac{9 (\sqrt{x} + 2)}{{(x^{\frac{1}{2}})}^{2} - 4}$

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

$- \frac{9 (\sqrt{x} + 2)}{x^{\frac{1}{2} \cdot 2} - 4}$

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

$- \frac{9 (\sqrt{x} + 2)}{x^{\frac{2}{2}} - 4}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- \frac{9 (\sqrt{x} + 2)}{x^{\frac{2}{2}} - 4}$

Rewrite the expression.

$- \frac{9 (\sqrt{x} + 2)}{x^{1} - 4}$

Simplify.

$- \frac{9 (\sqrt{x} + 2)}{x - 4}$