Simplifying a messy expression

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
Chasyesker
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Simplifying a messy expression

Postby Chasyesker » Mon Dec 16, 2013 9:31 pm

Need to combine and simplify the following expression

1/(7-4*SQRT(3)) - 1/(4*SQRT(3)-SQRT(47)) + 1/(SQRT(47) - SQRT(46)) - 1/(SQRT(46)-3*SQRT(5)) +

1/(3*SQRT(5)-2*SQRT(11)) ......... - 1/(SQRT(5) - 2)

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stapel_eliz
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Postby stapel_eliz » Mon Dec 16, 2013 11:24 pm

Chasyesker wrote:Need to combine and simplify the following expression

1/(7-4*SQRT(3)) - 1/(4*SQRT(3)-SQRT(47)) + 1/(SQRT(47) - SQRT(46)) - 1/(SQRT(46)-3*SQRT(5)) +

1/(3*SQRT(5)-2*SQRT(11)) ......... - 1/(SQRT(5) - 2)

Does the above mean the following?



Also, what is included in the ellipsis (the "dot dot dot") near the end? Is the pattern as follows (so, in particular, the sign on your last fraction should have been a "plus")?



When you reply, please show your work so far, and provide any rules,theorems, or other results from your class which you feel might be relevant. Thank you! :wink:

Chasyesker
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Re: Simplifying a messy expression

Postby Chasyesker » Tue Dec 17, 2013 4:10 pm

That's correct. I don't have access to the radical symbols so sorry for the messiness. I got as far as figuring out the pattern. The problem as stated has a negative sign for the last term but I think you are correct that it s/b +. The assigment sheets have ben known to be a bit sloppy when it comes to exactness.

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maggiemagnet
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Re: Simplifying a messy expression

Postby maggiemagnet » Tue Dec 17, 2013 5:25 pm

This might help a little:



So your fractions turn into:



The fractions start at n=48 and go to n=4.





So it comes down to 7+2=9. That seemed too easy, though, so I checked in Wolfram Alpha, and got the same thing, so I guess it's right!
:clap:

Chasyesker
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Re: Simplifying a messy expression

Postby Chasyesker » Tue Dec 17, 2013 8:10 pm

Yep,

That's what I eventually got and like you it seemed to easy but I guess they are not always hard. Thanks for spotting the wrong sign in the problem on the last term. That's how the sign was shown on the handout so I am going to assume it was a typo. I wrote it all out by hand and it should be "+". Hopefully I won't have to argue with the teacher.

Thanks again.


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