Question

Find the lcd of the given rational equation. 2x/x^-16+x-3/3x+12=1/x

A (x^2-16)(3x+12)
B 2x(x-3)
Cx(x^2-16)(3x+12)
D3x(x+4)(x-4)

Answer 1

The denominators of the rational equation are all divisors of the expression given by ...

... D. 3x(x +4)(x -4)

That is your lowest common denominator.

_____

The answer C could also serve as a common denominator, but it has an extra factor of x+4 that isn't necessary. Hence it is not the lowest common denominator.