# Thread: Rewrite expression with a rational denominator

1. ## Rewrite expression with a rational denominator

$\displaystyle \frac{\sqrt{5}-1}{\sqrt{5}+3}$ Rewrite the expression with a rational denominator

I start by multiplying top and bottom by $\displaystyle \sqrt{5}-3$

$\displaystyle =\frac{(\sqrt{5}-1)(\sqrt{5}-3)}{(\sqrt{5}+3)(\sqrt{5}-3)}$

Is my next step correct please?

$\displaystyle =\frac{5-3\sqrt{5}-\sqrt{5}+3}{5-9}$

2. Yeah, keep simplifying.

$\displaystyle \frac{5-3\sqrt{5}-\sqrt{5}+3}{5-9}$

$\displaystyle =\frac{8-4\sqrt{5}}{-4}$

$\displaystyle =-(2-\sqrt{5})$

$\displaystyle =\sqrt{5}-2$

3. Originally Posted by rowe
Yeah, keep simplifying.

$\displaystyle \frac{5-3\sqrt{5}-\sqrt{5}+3}{5-9}$

$\displaystyle =\frac{8-4\sqrt{5}}{-4}$

$\displaystyle =-(2-\sqrt{5})$

$\displaystyle =\sqrt{5}-2$
Thanks, I was not sure what to do with the -4 denominator, this is a big help.

However, I'm still confused because the answer given on the worksheet is $\displaystyle -\frac{(1+\sqrt{5})}{2}$

4. the answer should be $\displaystyle \sqrt{5}-2$,probably there were a typo on your worksheet.

5. Originally Posted by Meggomumsie
Thanks, I was not sure what to do with the -4 denominator, this is a big help.

However, I'm still confused because the answer given on the worksheet is $\displaystyle -\frac{(1+\sqrt{5})}{2}$
Look at the original expression. We know $\displaystyle \sqrt{5} > 1$, but the worksheet answer gives a negative number. I'm sure there's been a mistake.