Question 936599
Have not checked all your steps, but try Quotient Rule.


{{{(x^2*1-(x-2)*2x)/x^4}}}


{{{(x^2-2x^2+4x)/x^4}}}


{{{(x/x)(x-2x+4)/x^3}}}


{{{(-x+4)/x^3}}}


{{{highlight((4-x)/x^3)}}}


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Looking at YOUR answer,  
{{{4/x^3-1/x^2}}}
{{{4/x^3-x/x^3}}}   -------(elementary fractions skill)
{{{highlight((4-x)/x^3)}}}


The answer shown in your book might or might not be thought as more simplified, but the two answers ARE equivalent.