Question

Assuming that $3u + 12v\\eq0$, simplify $\dfrac{12u^3 + 48u^2v}{3u+12v}$.

Answer 1

4u²

Explanation:

`(12u^3 + 48u^2v)/(3u+12v)=(12u^2(u+4v))/(3(u+4v))=\boxed{4u^2}`

Common factors cancel from numerator and denominator. The one factor that might make the expression undefined is given as non-zero, so no additional restrictions apply.