Simplify (-5x)/(3- square root of x)

$\frac{- 5 x}{3 - \sqrt{x}}$

Move the negative in front of the fraction.

$- \frac{(5) x}{3 - \sqrt{x}}$

Multiply $\frac{5 x}{3 - \sqrt{x}}$ by $\frac{3 + \sqrt{x}}{3 + \sqrt{x}}$ .

$- (\frac{5 x}{3 - \sqrt{x}} \cdot \frac{3 + \sqrt{x}}{3 + \sqrt{x}})$

Multiply $\frac{5 x}{3 - \sqrt{x}}$ by $\frac{3 + \sqrt{x}}{3 + \sqrt{x}}$ .

$- \frac{5 x (3 + \sqrt{x})}{(3 - \sqrt{x}) (3 + \sqrt{x})}$

Expand the denominator using the FOIL method.

$- \frac{5 x (3 + \sqrt{x})}{9 + 3 \sqrt{x} - 3 \sqrt{x} - {\sqrt{x}}^{2}}$

Simplify.

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

$- \frac{5 x (3 + \sqrt{x})}{9 - {(x^{\frac{1}{2}})}^{2}}$

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

$- \frac{5 x (3 + \sqrt{x})}{9 - x^{\frac{1}{2} \cdot 2}}$

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

$- \frac{5 x (3 + \sqrt{x})}{9 - x^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- \frac{5 x (3 + \sqrt{x})}{9 - x^{\frac{2}{2}}}$

Rewrite the expression.

$- \frac{5 x (3 + \sqrt{x})}{9 - x^{1}}$

Simplify.

$- \frac{5 x (3 + \sqrt{x})}{9 - x}$