Very Basic Math question?How can I prove that r ( 1 − x ) 2 + r x x ( 1 − x ) = r x ( 1 − x ) 2 I have tried to prove that , but I could not , can someone help me please ?Thanks

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Very Basic Math question?How can I prove that      r          (      1      −      x              )        2              +            r      x              x      (      1      −      x      )        =      r          x      (      1      −      x              )        2            I have tried to prove that , but I could not , can someone help me please ?Thanks

torpa6d · Accepted Answer

If your original expression to prove is actually:      r          (      1      −      x              )        2              +      r          x      (      1      −      x      )        =      r          x      (      1      −      x              )        2            then it works out as follows:                              r                      (            1            −            x                          )              2                                      +                  r                      x            (            1            −            x            )                                              =                              r            x                                x            (            1            −            x                          )              2                                      +                              r            (            1            −            x            )                                x            (            1            −            x                          )              2                                                                        =                              r            x            +            r            −            r            x                                x            (            1            −            x                          )              2                                                                        =                  r                      x            (            1            −            x                          )              2                                          As observed, though, your original expression doesn&#039;t generally work.

Ryan Robertson · Accepted Answer

Multiply by   x  (  1  −  x      )    2   (assuming   x  ∉  {  0  ,  1  }), we get  r  x  +  r  x  (  1  −  x  )  =  r  .Or,  r  x  (  1  +  1  −  x  )  =  r  .Thus, unless   x  (  2  −  x  )  =  1 or   r  =  0, the above is not true.So   x  =  1 or   r  =  0 are only two possible cases when equation may hold.At   x  =  1, LHS and RHS of original equation are unbounded, so only possible case is   r  =  0

Very Basic Math question? How can I prove that r ( 1 &#x2212

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