# Rationalizing the denominator of a radical fraction

• March 18th 2012, 03:05 PM
chorzv32
Rationalizing the denominator of a radical fraction
This is for my trigonometry class but it's only a small portion of a bigger problem so I'm posting it here. Here is a picture of my issue:

http://i.imgur.com/cfxLe.png

How can I get that final answer? I know to rationalize a denominator I have to multiply both sides by the bottom radical, but that one seems more complicated. Help is appreciated.
• March 18th 2012, 03:25 PM
skeeter
Re: Rationalizing the denominator of a radical fraction
http://i.imgur.com/cfxLe.png

...

$\frac{15-7\sqrt{15}}{15+7\sqrt{15}} \cdot \frac{15-7\sqrt{15}}{15-7\sqrt{15}} =$

$\frac{15^2 - 14 \cdot 15 \sqrt{15} + 49 \cdot 15}{15^2 - 49 \cdot 15} =$

$\frac{15(15 - 14 \sqrt{15} + 49)}{15(15 - 49)} =$

$\frac{64 - 14 \sqrt{15}}{-34} =$

$\frac{7\sqrt{15}-32}{17}$
• March 18th 2012, 07:35 PM
Wilmer
Re: Rationalizing the denominator of a radical fraction
General:
(a - b) / (a + b) = (a^2 - 2ab + b^2) / (a^2 - b^2)

Your a is 15, your b is 7SQRT(15); throw 'em in there !