⚠ 6a is read as the product 6*a: for a power, write 6^a‖12ab is read as the product 12*a*b: for a power, write 12^(a*b)‖9a is read as the product 9*a: for a power, write 9^a‖3a is read as the product 3*a: for a power, write 3^a‖ab is read as the product a*b: for a power, write a^b; for the variable ab, write ab_

The original denominator must be nonzero: $3a^{3}b$ ≠ 0

Let's simplify: $\frac{6a^2+12ab-9a^4}{3a^{3}b}$

$\frac{3a·(2a+4b-3a^3)}{3a^{3}b}$

We divide $\frac{a}{a^3}$ by the common factor: $a$, which gives the new fraction: $\frac{1}{a^2}$

$\frac{3·(2a+4b-3a^3)}{3·a^{2}b}$

$\frac{2a+4b-3a^3}{a^{2}b}$

The fraction: $\frac{a}{a^2}$ simplifies by the common factor: $a$ into the new quotient: $\frac{1}{a}$

The fraction: $\frac{a^3}{a^2}$ simplifies by the common factor: $a^2$ into the new expression: $a$

$\frac{2}{ab}+\frac{4}{a^2}-\frac{3a}{b}$

▶Simplified form:   $-\frac{3a}{b}+\frac{2}{ab}+\frac{4}{a^2}$