Rewrite expression with a rational denominator

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October 12th 2009, 01:44 AM
Meggomumsie

Rewrite expression with a rational denominator

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

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

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

Is my next step correct please?

$=\frac{5-3\sqrt{5}-\sqrt{5}+3}{5-9}$
October 12th 2009, 02:08 AM
rowe

Yeah, keep simplifying.

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

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

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

$=\sqrt{5}-2$
October 12th 2009, 02:40 AM
Meggomumsie

Quote:

Originally Posted by rowe

Yeah, keep simplifying.

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

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

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

$=\sqrt{5}-2$

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

However, I'm still confused (Worried) because the answer given on the worksheet is $-\frac{(1+\sqrt{5})}{2}$
October 12th 2009, 03:04 AM
Raoh

the answer should be $\sqrt{5}-2$ ,probably there were a typo on your worksheet.
October 12th 2009, 03:07 AM
rowe

Quote:

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 (Worried) because the answer given on the worksheet is $-\frac{(1+\sqrt{5})}{2}$

Look at the original expression. We know $\sqrt{5} > 1$ , but the worksheet answer gives a negative number. I'm sure there's been a mistake.

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