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Math Help - How does this simplification work?

  1. #1
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    How does this simplification work?

    This is a calculus question, but I understand how the differentiation here works. What I don't understand is the simplification, which is generally algebra, so I posted it in this forum. I just can't figure out how they have done the simplification? I can get the end of the first line, but how they simplify it to the final outcome, can anyone help me understand? The second line I have no idea... how does -x^(3/5) suddenly become -5x/5x^(2/5)?
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  2. #2
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    Re: How does this simplification work?

    x^{3/5} is multiplied and divided by 5x^{2/5} to find the common denominator of the two terms.
    Thanks from lukasaurus
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  3. #3
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    Re: How does this simplification work?

    To put the terms in the same fraction they need to have the same common denominator: 5x^{2/5}

    So you must do:

    {-x^{3/5} = \frac{-x^{3/5} \cdot 5x^{2/5}}{5x^{2/5}} \ = \frac{-5x^{3/5 + 2/5}}{5x^{2/5}} \ = \frac{-5x^{5/5}}{5x^{2/5}} \ = \frac{-5x^1}{5x^{2/5}} \ = \frac{-5x}{5x^{2/5}}

    now as both terms in the equation have the same denominator then can be put into the same fraction:

    \frac{-5x}{5x^{2/5}} + \frac{3(4-x)}{5x^{2/5}} = \frac{-5x + 3(4-x)}{5x^{2/5}}

    which simplifies to:

    \frac{12-8x}{5x^{2/5}}
    Thanks from lukasaurus
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