Question

How do you add or subtract `x^3/(x^2-y^2 )+ (y^3)/( y^2-x^2)`?

Answer 1

We just need to find the lowest common denominator among these two fractions. However, we can easily see that one denominator is the opposite of the other (which means one is the "negative" of the other). This becomes clearer when we rewrite the operation:

`x^3/(x^2-y^2)+y^3/((-1)(x^2-y^2))`

So, now, we can consider as our lowest common denominator `(-1)(x^2-y^2)`.

Now, operating our sum...

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