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Math Help - Literal Equations help

  1. #1
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    Literal Equations help

    Could you guys help me with this maths methods question?

    x/(a-b)+2x(a+b)=1/a2-b2

    Solve for x
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  2. #2
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    Re: Literal Equations help

    Quote Originally Posted by Tehmo3 View Post
    Could you guys help me with this maths methods question?

    x/(a-b)+2x(a+b)=1/a2-b2

    Solve for x
    \frac{x}{a-b}+2x(a+b)=\frac{1}{a^2-b^2}

    x+2x(a+b)(a-b)=\frac{a-b}{(a-b)(a+b)}

    x\left(1+2(a^2-b^2)\right)=\frac{1}{a+b}

    x=\frac{1}{(a+b)\left(1+2(a^2-b^2)\right)}
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  3. #3
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    Re: Literal Equations help

    A slightly different way: \frac{x}{a-b}+ 2x(a- b)= x\left(\frac{1}{a- b}+ 2(a+ b)\right)= \frac{1}{a^2- b^2}= \frac{1}{(a- b)(a+ b)}
    Add the fractions on the left:
    x\left(\frac{1}{a- b}+ \frac{2(a+ b)(a- b)}{a- b}\right)= x\left(\frac{1+ 2(a^2- b^2)}{a- b}\right)= \frac{1}{(a- b)(a+ b)}

    Divide both sides by the fraction multiplying x:
    x= \frac{1}{(a- b)(a+ b)}\frac{a- b}{1+ 2(a^2- b^2)}= \frac{1}{(a+ b)(1+ 2(a^2- b^2))}
    because the two "a- b" factor cancel.
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