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Math Help - rationalize the denominator

  1. #1
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    rationalize the denominator

    Hi all,

    First of all hello! I am new here. Nice to meet you.

    I am taking an algebra class this semester after a very long break from math. I'm having a little trouble remembering some things and so far reading my textbook hasn't been very helpful.

    I have a problem that says "rationalize the denominator" and the problem is:

    3 + √x / 3 - √x

    I have come up with several different answers and I just need to know if I am on the right track. I multiplied both sides of the expression by the inverse of the denominator and used the FOIL method. I came up with 10√x^4 / √x^2 the last time I worked this expression out. Am I doing this correctly?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by uglygreencouch View Post
    Hi all,

    First of all hello! I am new here. Nice to meet you.

    I am taking an algebra class this semester after a very long break from math. I'm having a little trouble remembering some things and so far reading my textbook hasn't been very helpful.

    I have a problem that says "rationalize the denominator" and the problem is:

    3 + √x / 3 - √x

    I have come up with several different answers and I just need to know if I am on the right track. I multiplied both sides of the expression by the inverse of the denominator and used the FOIL method. I came up with 10√x^4 / √x^2 the last time I worked this expression out. Am I doing this correctly?
    to rationalize the denominator, you multiply by its conjugate over itself (so it's like multiplying by 1 so you don't change anything). that is, the same expression but you change the sign in the middle

    So you do the following:


    \frac {3 + \sqrt {x}}{3 - \sqrt {x}} = \frac {3 + \sqrt {x}}{3 - \sqrt {x}} \cdot \frac {3 + \sqrt {x}}{3 + \sqrt {x}}

    Can you take it from here?
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  3. #3
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    I'm a little worried about the word "inverse". I was hoping for "conjugate".

    The idea of rationalization is this: (a+b)(a-b) = a^2 - b^2 If a or b are square roots, this gets rid of the radicals. If you end up with some radicals, something went wrong.

    (3-\sqrt{3})(3+\sqrt{3}) = 3^{2} - (\sqrt{3})^{2} = 9 - 3 = 6
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  4. #4
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    I see what I was doing wrong! Thank you so much. I will learn this stuff if it kills me!
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