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

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

Simplify each term.

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

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

Combine and simplify the denominator.

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

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

Raise $\sqrt{x + 2}$ to the power of $1$ .

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

Raise $\sqrt{x + 2}$ to the power of $1$ .

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

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

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

Add $1$ and $1$ .

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

Rewrite ${\sqrt{x + 2}}^{2}$ as $x + 2$ .

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

To write $\sqrt{x + 2}$ as a fraction with a common denominator, multiply by $\frac{x + 2}{x + 2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Factor $\sqrt{x + 2}$ out of $\sqrt{x + 2} (x + 2) - 2 \sqrt{x + 2}$ .

Factor $\sqrt{x + 2}$ out of $- 2 \sqrt{x + 2}$ .

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

Factor $\sqrt{x + 2}$ out of $\sqrt{x + 2} (x + 2) + \sqrt{x + 2} \cdot - 2$ .

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

Subtract $2$ from $2$ .

$\frac{\sqrt{x + 2} (x + 0)}{x + 2}$

Add $x$ and $0$ .

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