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Math Help - Need help with simplifying rational expressions

  1. #1
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    Need help with simplifying rational expressions

    I can't figure out how to do these; can someone run me through the process? And please, pretend you're explaining to someone who's a complete and utter dunce when it comes to math.

    --

    Simplify the rational expression:

    95x2y
    35xy


    --
    Factor out the coefficients of x on the numerator and denominator of the rational expression:
    2x
    5x10


    --

    Simplify the rational expression:

    t2 + 3t18
    t212t + 27

    --


    Simplify the rational expression.
    (x2)
    8(x2) + 5



    --


    These were the ones I was having the most trouble on. I'm not asking you to do all of them for me (though feel free if you want), I just need to have it slowly explained how.
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  2. #2
    MHF Contributor

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    Re: Need help with simplifying rational expressions

    Quote Originally Posted by InDrk View Post
    I can't figure out how to do these; can someone run me through the process? And please, pretend you're explaining to someone who's a complete and utter dunce when it comes to math.
    There would be no point in trying to explain to a "complete and utter dunce". I would prefer to assume an intelligent person who has little background in algebra.

    --

    Simplify the rational expression:

    95x2y
    35xy
    I presume you know that \frac{a}{a}= 1 (as long as a\ne 0).
    95= 5(19) and 35= 5(7) is \frac{95}{35}= \frac{5}{5}\frac{19}{7}= \frac{19}{7}
    \frac{x^2}{x}= x\frac{x}{x}= x
    \frac{y}{y}= 1
    so \frac{95x^2y}{35xy}= \frac{19x}{7}

    --
    Factor out the coefficients of x on the numerator and denominator of the rational expression:
    2x
    5x10

    Okay, the "coefficient of x" in the numerator is -1 and 2= (-1)(-2). 2- x= -2(-1)+ x(-1)= -1(-2+ x)= -1(x- 2). The coefficient of x in the denominator 5: 5x- 10= 5(x-2). So, as long as x is not 2, we cancel the "x- 2" in numerator and denominator. That is \frac{2- x}{5x- 10}= \frac{-1(x- 2)}{5(x- 2)}= \frac{-1}{5} which could also be written as -\frac{1}{5}.

    --

    Simplify the rational expression:
    t2 + 3t18
    t212t + 27
    Start by trying to factor. 18= 2(3)(3) can be factored with two factors as either 2(9) or 6(3). 9- 2= 7, not 3 but 6- 3= 3. So t^2+ 3x- 18= (t+ 6)(t- 3).  27= 3(3)(3) can be factored with two factors are 3(9) and 9+ 3= 12! So t^2- 12t+ 27= (t- 3)(t- 9). So the fraction is \frac{t^2+ 3t- 18}{t^2- 12t+ 27}= \frac{(t+ 6)(t- 3)}{(t- 3)(t- 9)}. Now you can cancel the two "t- 3" terms.


    --


    Simplify the rational expression.
    (x2)
    8(x2) + 5
    The denominator is (x- 2)+ 5= x+ 3 which has no factors in common with x- 2. So we cannot cancel anything and only have
    \frac{x- 2}{x+ 3} as the simplest form.


    --


    These were the ones I was having the most trouble on. I'm not asking you to do all of them for me (though feel free if you want), I just need to have it slowly explained how.
    Last edited by HallsofIvy; July 18th 2013 at 02:18 PM.
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