Question

Least common denominator?

Answer 1

`\large\boxed{(s-2)(s+2)(s-3)=(s^2-4)(s-3)=s^3-3s^2-4s+12}`

Explanation:

`s^2-4=s^2-2^2=(s-2)(s+2)\\\\\text{used}\ a^2-b^2=(a-b)(a+b)\\\\s^2-5s+6=s^2-2s-3s+6=s(s-2)-3(s-2)=(s-2)(s-3)\\\\\text{Therefore}\ LCD(s^2-4,\ s^2-5s+6)=(s-2)(s+2)(s-3)`