How do you simplify #(x-3)/(-x^3+3x^2)*(x^2+2x+1)#?

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Answer 1 · 2017-05-24T14:03:47

#-1 - frac{2x + 1}{x^2}#

#frac{x - 3}{(-x + 3) x^2} * (x^2 + 2x + 1)#

#= - frac{1}{x^2} * (x^2 + 2x + 1)#

#= -1 + frac{-2x - 1}{x^2}#

Answer 2 · 2017-05-24T16:07:26

#(-x^2-2x-1)/x^2#

#(x-3)/(-x^3+3x^2)*x^2+2x+1#

#:.=cancel(x-3)^1/(-x^2cancel((x-3)^1))*x^2+2x+1#

#:.=1/(-x^2)*x^2+2x+1#

#:.=(x^2+2x+1)/-x^2#

#:.=((x^2+2x+1)/-x^2)*(-x^2)/-x^2#

#:.=(-x^2)/(-x^2)=1#

#:.=(cancel(-x^2)^color(blue)(-1)(x^2+2x+1))/cancel(x^4)^color(blue)(x^2)#

#:.=(-1(x^2+2x+1))/x^2#

#:.=color(blue)((-x^2-2x-1)/x^2#