Question

lim x→-1 (x^3+3x^2-x-3)/(x^3-x^2+2)

Answer 1

Pronto, na caneta e papel sempre fica mais fácil de desenvolver.

Answer 2

x³+3x²-x-3   |  x+1

-x³-x²           |    x²   +2x   -3

2x²-x-3

-2x²-2x

-3x-3

3x+3

x³+3x²-x-3 =(x+1)*(x²+2x-3)

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x³-x²+2 |  x+1

-x³-x²    |  x²-2x +2

-2x²+2

+2x²+2x

2x+2

-2x-2

x³-x²+2 =(x+1)*( x²-2x +2)

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Lim (x^3+3x^2-x-3)/(x^3-x^2+2)

x-->-1

Lim  (x+1)*(x²+2x-3)/(x+1)*( x²-2x +2)

x-->-1

Lim  (x²+2x-3)/( x²-2x +2) =(1-2-3)/(1+2+2)= -4/5

x-->-1