# How do you simplify 3/(sqrt(3)-3)?

Feb 15, 2015

Actually there is a much easier way to do this:

First i will rewrite this to ensure clarity:

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

So now lets remove common factor

$\frac{\sqrt{3} \left(\sqrt{3}\right)}{\sqrt{3} \left(1 - \sqrt{3}\right)}$

Now leta get rid of the $\sqrt{3}$ in the denominator and numerator:

$\frac{\sqrt{3}}{1 - \sqrt{3}}$

Now we shall rationalize:

$\frac{\sqrt{3}}{1 - \sqrt{3}} \cdot \frac{1 + \sqrt{3}}{1 + \sqrt{3}}$

That should be

$\frac{\sqrt{3} + 3}{1 - 3} = \frac{\sqrt{3} + 3}{-} 2$