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Math Help - Engineering Maths help

  1. #1
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    Engineering Maths help

    I am having a blond moment. Cant see how this is done but I know it is simple, Can someone explain please.
    I have a revision Question at Uni. part of it says Multiply the top and Botom of the equation by 1+4s but i cant see how it works. please see the attachment


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  2. #2
    Senior Member abhishekkgp's Avatar
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    Quote Originally Posted by bobbych View Post
    I am having a blond moment. Cant see how this is done but I know it is simple, Can someone explain please.
    I have a revision Question at Uni. part of it says Multiply the top and Botom of the equation by 1+4s but i cant see how it works. please see the attachment

    the fact that  \frac{a}{b}=\frac{ax}{bx} if   b,x \neq 0 has been used.
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  3. #3
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    So here's what yo have:

    \frac{\frac{6}{1 + 4s}}{1 + (\frac{6}{1 + 4s})3} = \frac{\frac{6}{1 + 4s}}{1 + \frac{18}{1 + 4s}}

    If simplifying is what you are trying to do, then yes you can multiply the top and bottom by  1 + 4s will help.

    What you have in your attachment is:

     \frac{6}{1 + 4s + 18} = \frac{6}{4s + 19}

    Although this is a true statement, I don't think you did it right.

    I think the numerator is correct, but when you multiply the denominator by  1 + 4s it needs to look like:

     ((1 + (\frac{6}{1 + 4s})3)(1 + 4s)

    In other words you need to multiply it like
     (a + b)(c + d) = ac + ad + bc + bd

    So try this out and see what you get; hope this helps.
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  4. #4
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    When dealing with fractions, it's nearly always best to have a common denominator. This is even more true when you have fractions of fractions.

    You have \displaystyle \begin{align*}\frac{\frac{6}{1 + 4s}}{1 + \frac{18}{1 + 4s}} &= \frac{\frac{6}{1 + 4s}}{\frac{1 + 4s + 18}{1 + 4s}}\\ &= \frac{\frac{6}{1 + 4s}}{\frac{19 + 4s}{1 + 4s}} \\ &= \frac{6}{1 + 4s} \cdot \frac{1 + 4s}{19 + 4s} \\ &= \frac{6}{19 + 4s}\end{align*}
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