As a software developer for an educational technology company, you are outlining the logic for a program that tutors students on simplifying rational expressions. The test case involves simplifying the expression $\frac{v}{v+1} + \frac{3}{v-1} - \frac{6}{v^2-1}$. To properly program the step-by-step hints for the user, arrange the following calculation steps in the correct order.

As a data analyst for a logistics firm, you are simplifying a formula that represents the cost-efficiency of a delivery route: $\frac{v}{v+1} + \frac{3}{v-1} - \frac{6}{v^2-1}$. To successfully combine these terms for a summary report, what is the Least Common Denominator (LCD) you must identify?

As an Inventory Control Specialist, you use a specific formula to manage restocking schedules. The formula involves simplifying the expression: $\frac{v}{v+1} + \frac{3}{v-1} - \frac{6}{v^2-1}$ To ensure the formula is used correctly across the department, match each component of the simplification process with its corresponding mathematical expression based on the standard solution steps.

Final Simplification Step in Rational Expressions

As an administrative assistant in a medical clinic, you are helping a physician simplify a dosage adjustment formula represented by the expression $\frac{v}{v+1} + \frac{3}{v-1} - \frac{6}{v^2-1}$. The physician has already combined the terms and factored the numerator to reach the intermediate step $\frac{(v+3)(v-1)}{(v-1)(v+1)}$. To finalize the simplification and reach the result of $\frac{v+3}{v+1}$, you must identify the common factor that is present in both the numerator and the denominator. The common factor is ____.