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Math Help - Help with rational expressions plz

  1. #1
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    Help with rational expressions plz

    If anybody could help, I have a math exam tomorrow, and I'm working on the review...but I've been having alot of trouble. Usually I can figure this stuff out by studying my notes...but I'm at a loss. Any help would be appreciated. The first three are problems that I don't understand, the rest are ones that I've completed, but I'm not sure if they're right.

    1.  x^2+x=20

    2. Solve by quadratic formula:

     2x^2-5x=2

    3. Solve by completing the square:

     x^2+8x-9=0


    And the ones that I've completed, but not sure if they're right...I would appreciate if you could check these out.

    1.  6y \sqrt{27x^3y} - 3x \sqrt{12xy^3} + xy \sqrt{4xy}

    I got:

     12xy \sqrt{3xy} + 2xy \sqrt{xy}

    2.  (4 \sqrt{x} + 3 \sqrt{y})(2 \sqrt{x} - 5 \sqrt{y})


    I got:

     8x-14 \sqrt{xy} - 15y

    3.  \frac{\sqrt 75a^8b^5}{\sqrt 5ab^2}

    I got:

     b \sqrt{15a^7b}
    Last edited by ohiostatefan; July 19th 2009 at 04:42 PM.
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  2. #2
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    Quote Originally Posted by ohiostatefan View Post
    1.  x^2+x=20
     x^2+x-20=0

    factors of 20 that add to give 1 are -4 & -5 so

    (x-4)(x+5)

    Quote Originally Posted by ohiostatefan View Post


    2. Solve by quadratic formula:

     2x^2-5x=2
     2x^2-5x-2=0

    x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}

    in your case a = 2, b= -5 and c = -2

    Quote Originally Posted by ohiostatefan View Post


    3. Solve by completing the square:

     x^2+8x-9=0
     (x^2+8x+16)-9-16=0

     (x+4)^2-9-16=0

     (x+4)^2-25=0

    the square is now complete, now solve!
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  3. #3
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    Quote Originally Posted by ohiostatefan View Post
    If
    And the ones that I've completed, but not sure if they're right...I would appreciate if you could check these out.

    1.  6y \sqrt{27x^3y} - 3x \sqrt{12xy^3} + xy \sqrt{4xy}

    I got:

     12xy \sqrt{3xy} + 2xy \sqrt{xy}

    2.  (4 \sqrt{x} + 3 \sqrt{y})(2 \sqrt{x} - 5 \sqrt{y})


    I got:

     8x-14 \sqrt{xy} - 15y

    3.  \frac{\sqrt 75a^8b^5}{\sqrt 5ab^2}

    I got:

     b \sqrt{15a^7b}
    I agree with all your answers except the last problem, should be   \sqrt{15}a^7b^3
    Last edited by pickslides; July 19th 2009 at 05:44 PM. Reason: typo
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  4. #4
    Senior Member Stroodle's Avatar
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    Would you not be required to express the answer in its simplest form?

    i.e. a^3 b\sqrt{15ab}

    Thanks

    *edit - Actually is the question supposed to be \frac{\sqrt{75}a^8b^5}{\sqrt{5}ab^2}? Because then the answer would be a^7b^3\sqrt{15}. The above would be the answer to \frac{\sqrt{75a^8b^5}}{\sqrt{5ab^2}}. As it's written the question looks like \frac{\sqrt{7}\times 5a^8b^5}{\sqrt{5}ab^2} which =a^7b^3\sqrt{35}.
    Last edited by Stroodle; July 19th 2009 at 05:50 PM.
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