Question:

How can u simplify this expression...?

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(x(1-2x)^(-3/2))+((1-2x)^2) ?

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  1. =  (x(1-2x)^(-3/2)) + (1-2x)²

    =  x / (1 - 2x)^3/2   +   (1 - 2x)²    (now take a common denominator).

    =  [x  +  (1 - 2x)^3/2 * (1 - 2x)² ]/ (1 -2x)^3/2

    =  [x  +  (1 - 2x)^7/2] / (1 - 2x)^3/2  


  2. Remember x^-a = 1/(x^a)

    so (1-2x)^(-3/2)= 1/(1-2x)^(3/2)

    Now (1-2x)^(3/2)=sqrt (1-2x)^3, since sqrt x^2 =x then sqrt x^3=xsqrtx therefore  

    sqrt[(1-2x)^3]= (1-2x)*sqrt(1-2x)

    First term is x/[(1-2x)*sqrt(1-2x)]

    Find common denominator: [(1-2x)*sqrt(1-2x)]

    Now we have:

    [x+(1-2x)^2[(1-2x)*sqrt(1-2x)]]/[(1-2x... which is worst

    Answer is no it is already simple

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