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

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To simplify the expression x^3/(x^2-y^2) + y^3/(y^2-x^2), we can factor the denominators and then find a common denominator.

First, let's factor the denominators: x^2 - y^2 can be factored as (x + y)(x - y) y^2 - x^2 can be factored as (y + x)(y - x)

Now, let's find the common denominator: The common denominator is (x + y)(x - y)(y + x)(y - x)

Next, let's rewrite the expression with the common denominator: x^3/(x^2-y^2) + y^3/(y^2-x^2) = (x^3 * (y + x)(y - x))/((x + y)(x - y)(y + x)(y - x)) + (y^3 * (x + y)(x - y))/((x + y)(x - y)(y + x)(y - x))

Now, let's combine the numerators: (x^3 * (y + x)(y - x) + y^3 * (x + y)(x - y))/((x + y)(x - y)(y + x)(y - x))

Finally, let's simplify the numerator: (x^3 * (y^2 - x^2) + y^3 * (x^2 - y^2))/((x + y)(x - y)(y + x)(y - x))

Therefore, the simplified expression is (x^3 * (y^2 - x^2) + y^3 * (x^2 - y^2))/((x + y)(x - y)(y + x)(y - x)).

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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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