Rationalizing the denominator of 4 / (sqrt[7] - 1)

[debih001]

This is my first post, so please excuse me if I don't post this correctly. I'll do my best to make it clear. The problem is as follows:

. . .Rationalize the denominator of 4 / (sqrt[7] - 1)

I know I multiply top and bottom by the conjugate of sqrt[7] - 1, which is sqrt[7] + 1, and from there I get:

. . .( 4(sqrt[7] + 1) ) / ((sqrt[7])^2 - 1^2)

...which simplifies to:

. . .( 4 sqrt[7] - 4 ) / (7 - 1)

. . .( 4 sqrt[7] - 4) / 6

Here's where my problem lies: I simplify this to:

. . .( 2 sqrt[7] + 4 ) / 3

...but the book shows the answer as:

. . .( 2sqrt[7] + 2 ) / 3

How did that second "2" get simplified?

Thank you. I hope this is clear; I'm doing my best!
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Edited by stapel -- Reason for edit: clarifying formatting

 

[skeeter]

\(\displaystyle \L \frac{4}{\sqrt{7} - 1} \cdot \frac{\sqrt{7} + 1}{\sqrt{7} + 1} = \frac{4(\sqrt{7}+1)}{(\sqrt{7}-1)(\sqrt{7}+1)}=\)

\(\displaystyle \L \frac{4\sqrt{7} + 4}{6} = \frac{2(2\sqrt{7} + 2)}{2\cdot3} = \frac{2\sqrt{7} + 2}{3}\)

 

[Denis]

WHY did you create a 2nd thread for the SAME problem? :twisted:

> ( 4(sqrt[7] + 1) ) / ((sqrt[7])^2 - 1^2)
> ..which simplifies to:
> . .( 4 sqrt[7] - 4 ) / (7 - 1)
> . .( 4 sqrt[7] - 4) / 6

LEAVE the 4 outside the brackets:
4[sqrt(7) + 1] / 6
now simplify:
2[sqrt(7) + 1)] / 3
You can leave it like that, or perform the multiplication:
[2sqrt(7) + 2] / 3
In other words: KEEP IT SIMPLE :wink:

 

[debih001]

I didn't think I started a new thread.....told you, new at this.

 

[stapel]

I didn't think I started a new thread.....told you, new at this.

You did; the orphaned reply has since been deleted (since, without the originating thread, it made no sense).

To reply to a topic ("thread"), click on the "post reply" button. Clicking on the "new topic" button does just that: it starts a new (unconnected) topic.

I apologize for any confusion.

Eliz.