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

Answer 1

Eva Adamson

#-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}#

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Answer 2

Eva Adamson

#(-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#

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Answer 3

Isaiah Anthony

To simplify the expression (x-3)/(-x^3+3x^2)*(x^2+2x+1), we can first factor the denominator -x^3+3x^2 as -x^2(x-3). Then, we can simplify the expression as follows:

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

Therefore, the simplified expression is (x^2+2x+1)/x^2.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.