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Math Help - Operations on Real Numbers and Rational Equations

  1. #1
    Mad
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    Operations on Real Numbers and Rational Equations

    [(x^2n + x^n)/(2x - 2)] / [(4x^n + 4)/(x^n+1 - x^n)]


    NOTE: (x^2n + x^n) : The power isn't 2, it's 2n.
    (x^n+1 - x^n) : The power isn't n, it's n+1.

    Sorry, I don't know how to get it to work properly.


    [(x-1)/(x+1) - (x+1)/(x-1)] / [(x-1)/(x+1) + (x+1)/(x-1)]



    Last two problems.
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  2. #2
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    [(x^2n + x^n)/(2x - 2)] / [(4x^n + 4)/(x^n+1 - x^n)]
    \frac {\frac {x^{2n}+x^n}{2x-2}}{\frac {4x^n+4}{x^{n+1}-x^n}}

    to get more than one thingy in a superscript, surround them with curly brackets eg x^{2n}.

    Just factorise all of the brackets then cancel. Remember that x^{2n} = x^n*x^n and \frac {a/b}{c/d} = \frac {ad}{bc}
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  3. #3
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    <br />
\frac{{\frac{{x^{2n}  + x^n }}<br />
{{2x - 2}}}}<br />
{{\frac{{4x^n  + 4}}<br />
{{x^{n + 1}  - x^n }}}} = \frac{{x^{2n}  + x^n }}<br />
{{2x - 2}} \cdot \frac{{x^{n + 1}  - x^n }}<br />
{{4x^n  + 4}} = \frac{{x^n \left( {x^n  + 1} \right)}}<br />
{{2\left( {x - 1} \right)}} \cdot \frac{{x^n \left( {x - 1} \right)}}<br />
{{4\left( {x^n  + 1} \right)}} = \frac{{x^n x^n }}<br />
{{\left( 2 \right)\left( 4 \right)}} = \frac{{x^{2n} }}<br />
{8}<br />




    <br />
\boxed{ <br />
  {\text{Let }}a = x - 1\text{; <br />
}<br />
  {\text{      }}b = x + 1 }<br />
:


    \frac{{\frac{a}<br />
{b} - \frac{b}<br />
{a}}}<br />
{{\frac{a}<br />
{b} + \frac{b}<br />
{a}}} = \frac{{\frac{{a^2  - b^2 }}<br />
{{ab}}}}<br />
{{\frac{{a^2  + b^2 }}<br />
{{ab}}}}  = \frac{{a^2  - b^2 }}<br />
{{ab}} \cdot \frac{{ab}}<br />
{{a^2  + b^2 }} = \frac{{a^2  - b^2 }}<br />
{{a^2  + b^2 }} = \frac{{\left( {a + b} \right)\left( {a - b} \right)}}<br />
{{a^2  + b^2 }}

    \frac{{\left( {a + b} \right)\left( {a - b} \right)}}<br />
{{a^2  + b^2 }} = \frac{{\left( {\left( {x - 1} \right) + \left( {x + 1} \right)} \right)\left( {\left( {x - 1} \right) - \left( {x + 1} \right)} \right)}}<br />
{{\left( {x - 1} \right)^2  + \left( {x + 1} \right)^2 }} = \frac{{\left( {2x} \right)\left( { - 2} \right)}}<br />
{{\left( {x^2  - 2x + 1} \right) + \left( {x^2  + 2x + 1} \right)}} =  \frac{{ - 4x}}<br />
{{2x^2  + 2}} = \frac{{ - 2x}}<br />
{{x^2  + 1}}
    Last edited by xifentoozlerix; March 6th 2008 at 01:14 AM.
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