As a data analyst reviewing the logic behind a supply chain efficiency algorithm, you are analyzing a module that automates the simplification of the cost-variance expression $\frac{3}{z+3} - \frac{6z}{z^2-9}$ (where $z$ represents the number of supply zones). To audit the software's process, recall the standard mathematical procedure for subtracting these rational expressions by arranging the simplification steps in the correct chronological order.

As a junior analyst for a logistics firm, you are auditing a script used to calculate zone-based delivery fees. The script performs the subtraction $\frac{3}{z+3} - \frac{6z}{z^2-9}$, where $z$ represents the number of delivery zones. Match each mathematical component from the audit with its correct functional role in the simplification process.

In your role as a data auditor, you are verifying the initial steps of a formula simplification used in a zone-based shipping model. For the expression $\frac{3}{z+3} - \frac{6z}{z^2-9}$, recall the factored form of the second denominator, $z^2 - 9$, which is necessary to determine the Least Common Denominator (LCD).

Inventory Formula Optimization

As a data analyst for a shipping firm, you are verifying a cost-optimization formula: $\frac{3}{z+3} - \frac{6z}{z^2-9}$. To subtract these rational expressions, you first identify the Least Common Denominator as $(z+3)(z-3)$. To rewrite the first term, $\frac{3}{z+3}$, with this common denominator, you must multiply both its numerator and denominator by the missing factor ____.