Rationalizing the Denominator

[dwlniles]

I have been stuck on this problem for hours and cannot figure it out.

15-7?15 /15+7?15

I think I need to multiply the numerator and the denominator by 15-7?15, but then I just get stuck.
The answer says it is 7?15 -32 / 17, but I have no clue how they are getting this answer.
Can someone please explain this to me?

 

[soroban]

Hello, dwlniles!

No one is answering because they don't understand what you wrote.

Fortunately, I speak fluent Klingon . . .

\(\displaystyle \text{Rationalize: }\;\frac{15-7\sqrt{15}}{15 + 7\sqrt{15}}\)

\(\displaystyle \text{Multiply top and bottom by }(15 - 7\sqrt{15})\)

. . \(\displaystyle \frac{15-7\sqrt{15}}{15+7\sqrt{15}} \cdot\frac{15-7\sqrt{15}}{15-7\sqrt{15}} \;\;=\;\; \frac{225 - 105\sqrt{15} - 105\sqrt{15} + 735}{225 - 105\sqrt{15} + 105\sqrt{15} - 735} \;\;=\;\;\frac{960 - 210\sqrt{15}}{-510}\)

\(\displaystyle \text{Divide top and bottom by }-30\!:\;\;\frac{-32 + 7\sqrt{15}}{17} \;\;=\;\;\frac{7\sqrt{15} - 32}{17}\)

 

[dwlniles]

LOL, thank you so much for showing me and understanding the problem

 

[Deleted member 4993]

I have been stuck on this problem for hours and cannot figure it out.

15-7?15 /15+7?15

I think I need to multiply the numerator and the denominator by 15-7?15, but then I just get stuck.
The answer says it is 7?15 -32 / 17, but I have no clue how they are getting this answer.
Can someone please explain this to me?

You should have posted the problem as:

(15-7?15) /(15+7?15)

In addition, you did not tell us what you needed to do....

Those parentheses are very important - without those it becomes Klingon-speak.