x/x^3+y^3 , x/x+y
The LCD is
x^3 + y^3 = (x + y)(x2 - xy + y2)
The lowest common denominator is therefore x^3 + y^3. (x+y) is a factor of both denominators
x/(x+y) = [x(x^2 -xy + y^2)]/(x^3 + y^3)
In order to find the least common denominator (LCD) for the given expressions, it is necessary to factor the denominators.
For the first expression, x/x^3 + y^3, the denominator x^3 can be factored as x * x * x.
For the second expression, x/x + y, the denominator x can be factored as x * 1.
To find the LCD, we need to take into account the common factors between the denominators and any unique factors. In this case, the common factor is x. Thus, the LCD is x * x * x * 1, which can be written as x^3.
So, the LCD for the given expressions is x^3.