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Math Help - simplify

  1. #1
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    simplify

    Simplify this :

     \frac{\frac{1}{2}mv^2}{\frac{1}{2}m(\frac{m^2u^2}{  M^2})}

     =\frac{u^2}{\frac{m^2u^2}{M^2}}

    =\frac{M^2}{m^2}

     =\frac{M}{m}

    i doubt if i am correct (the last 2 steps) , is it possible to change this
    \frac{M^2}{m^2} to \frac{M}{m}

    THanks ..
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  2. #2
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    Quote Originally Posted by alphabeta View Post
    Simplify this :

     \frac{\frac{1}{2}m{\color{red}v^2}}{\frac{1}{2}m(\  frac{m^2u^2}{M^2})}

     =\frac{\color{red}u^2}{\frac{m^2u^2}{M^2}}.......<<<<<<< are you sure?

    =\frac{M^2}{m^2}

     =\frac{M}{m}

    i doubt if i am correct (the last 2 steps) , is it possible to change this
    \frac{M^2}{m^2} to \frac{M}{m}

    THanks ..
     \frac{v^2}{\frac{m^2u^2}{M^2}} = \frac{M^2 \cdot v^2}{m^2u^2} = \left(\frac{M \cdot v}{m \cdot u}  \right)^2

    You only can cancel the Mms if M = m.
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  3. #3
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    Quote Originally Posted by earboth View Post
     \frac{v^2}{\frac{m^2u^2}{M^2}} = \frac{M^2 \cdot v^2}{m^2u^2} = \left(\frac{M \cdot v}{m \cdot u} \right)^2

    You only can cancel the Mms if M = m.

    sorry , it should be :
     <br /> <br />
\frac{\frac{1}{2}mu^2}{\frac{1}{2}M(\frac{m}{M}u)^  2}<br />
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  4. #4
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    Quote Originally Posted by alphabeta View Post
    sorry , it should be :
     <br /> <br />
\frac{\frac{1}{2}mu^2}{\frac{1}{2}M(\frac{m}{M}u)^  2}<br />
    In this case your result is OK:

     <br /> <br />
\frac{\frac{1}{2}mu^2}{\frac{1}{2}M(\frac{m}{M}u)^  2} = \frac{\frac{1}{2}m u^2}{\frac{1}{2}M \cdot \left(\frac{m^2}{M^2}\cdot u^2\right)} = \frac{\frac{1}{2}m u^2}{\frac{1}{2}m u^2 \cdot \frac{m}{M}} = \dfrac Mm<br />
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