A student in an algebra review course is simplifying the following expression:

$\frac{6x^2-x+20}{x^2-81} - \frac{5x^2+11x-7}{x^2-81}$

Arrange the steps below in the correct chronological order to complete the subtraction and simplify the result.

As part of a continuous improvement training program, you are reviewing algebraic models used to calculate the difference in projected regional costs. The difference is modeled by the following expression: $\frac{6x^2-x+20}{x^2-81} - \frac{5x^2+11x-7}{x^2-81}$. When performing the first step of subtracting the rational expressions, you must recall the procedural rule to distribute the subtraction operation across the entire second numerator. Which of the following correctly displays the combined numerator immediately after distributing the negative sign, but before combining any like terms?

A logistics manager is simplifying a formula that represents the difference in delivery times between two regional routes: $\frac{6x^2-x+20}{x^2-81} - \frac{5x^2+11x-7}{x^2-81}$. True or False: When this expression is simplified to its lowest terms, the denominator of the resulting rational expression is $x+9$.

A logistics coordinator is comparing two cost-efficiency models represented by the rational expressions $\frac{6x^2-x+20}{x^2-81}$ and $\frac{5x^2+11x-7}{x^2-81}$. To find the difference between these models, the coordinator must subtract the two expressions and simplify. Match each algebraic component of the simplification process to its corresponding form.

Intermediate Simplification of Quality Control Models