Question

Combine the following rational expressions.
1/x-y-3/x^3-y^3=1/x-y-3/(x^2+xy+y^2)(x-y)

Answer 1

I will assume you meant:
1/(x-y) - 3/(x^3-y^3) + 1/(x-y) - 3/((x^2+xy+y^2)(x-y))

you should realize that
x^3 - y^3 = (x-y)(x^2 + xy + y^2)
so there is your LCD
Also notice that the first and third time are like terms, as is the 2nd and the last

so you can first of all combine them into
2/(x-3) - 6/((x^2+xy+y^2)(x-y))

carry on