Simplify x/(x+ square root of 3)

$\frac{x}{x + \sqrt{3}}$

Step 1

Multiply $\frac{x}{x + \sqrt{3}}$ by $\frac{x - \sqrt{3}}{x - \sqrt{3}}$ .

$\frac{x}{x + \sqrt{3}} \cdot \frac{x - \sqrt{3}}{x - \sqrt{3}}$

Step 2

Multiply $\frac{x}{x + \sqrt{3}}$ by $\frac{x - \sqrt{3}}{x - \sqrt{3}}$ .

$\frac{x (x - \sqrt{3})}{(x + \sqrt{3}) (x - \sqrt{3})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{x (x - \sqrt{3})}{x^{2} + x (- \sqrt{3}) + \sqrt{3} x - {\sqrt{3}}^{2}}$

Step 4

Simplify.

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\frac{x (x - \sqrt{3})}{x^{2} - {(3^{\frac{1}{2}})}^{2}}$

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

$\frac{x (x - \sqrt{3})}{x^{2} - 3^{\frac{1}{2} \cdot 2}}$

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

$\frac{x (x - \sqrt{3})}{x^{2} - 3^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x (x - \sqrt{3})}{x^{2} - 3^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{x (x - \sqrt{3})}{x^{2} - 3^{1}}$

Evaluate the exponent.

$\frac{x (x - \sqrt{3})}{x^{2} - 1 \cdot 3}$

Multiply $- 1$ by $3$ .

$\frac{x (x - \sqrt{3})}{x^{2} - 3}$