# What is the limit of #(x^3 -1)/(x^2+2x-3)# as x approaches 1?

The numerator of the fraction can be factored using the formula for the difference of two cubes

This means that you can write

Now focus on the denominator, which can be factored to get

Your limit will now be

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The limit of (x^3 -1)/(x^2+2x-3) as x approaches 1 is 0.

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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.

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.

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.

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