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Math Help - Equations::::

  1. #1
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    Equations::::

    i am having this problem and i couldn't prove that the left side equals the right side
    i don't know what exactly that i am missing !!
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  2. #2
    MHF Contributor

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    Re: Equations::::

    Step one is to recognize that 3^{-x}= \frac{1}{3^x} so that \frac{1}{3^{-x}}= \frac{1}{\frac{1}{3^x}}= 3^x. So \frac{3^x}{5}- \frac{2}{3^{-x}}= \frac{3^x}{5}- 2(3^x). Now get common denominators by multiplying numerator and denominator of the last fraction by 5: \frac{3^x}{5}- \frac{10(3^x)}{5}= \frac{-9(3^x)}{5}= -\frac{3^2(3^x)}{5}= -\frac{3^{2+ x}}{5}.
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