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

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

Step 1

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

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

Step 2

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

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

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

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

Step 5

Cancel the common factor of $2 - x$ and $x - 2$ .

Rewrite $2$ as $- 1 (- 2)$ .

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

Factor $- 1$ out of $- x$ .

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

Factor $- 1$ out of $- 1 (- 2) - (x)$ .

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

Reorder terms.

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

Cancel the common factor.

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

Divide $- 1 (\sqrt{x + 2} + 2)$ by $1$ .

$- 1 (\sqrt{x + 2} + 2)$

Step 6

Rewrite $- 1 (\sqrt{x + 2} + 2)$ as $- (\sqrt{x + 2} + 2)$ .

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

Step 7

Apply the distributive property.

$- \sqrt{x + 2} - 1 \cdot 2$

Step 8

Multiply $- 1$ by $2$ .

$- \sqrt{x + 2} - 2$