Reorder and .

Divide the numerator and denominator by the highest power of in the denominator, which is .

Simplify each term.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Simplify each term.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Split the limit using the Limits Quotient Rule on the limit as approaches .

Split the limit using the Sum of Limits Rule on the limit as approaches .

Since its numerator approaches a real number while its denominator is unbounded, the fraction approaches .

Since its numerator approaches a real number while its denominator is unbounded, the fraction approaches .

Split the limit using the Sum of Limits Rule on the limit as approaches .

Since its numerator approaches a real number while its denominator is unbounded, the fraction approaches .

Evaluate the limit of which is constant as approaches .

Add and .

Simplify the denominator.

Multiply by .

Add and .

Add and .

Divide by .

Evaluate limit as x approaches infinity of (1-x^2)/(x^3-x+1)