As an inventory analyst, you are calculating the net change in warehouse stock. The influx rate of a product is modeled by the expression $\frac{7}{d}$ and the outflow rate is modeled by $\frac{5}{-d}$, where $d$ is a variable representing time in days. To find the total net rate, you must evaluate the sum $\frac{7}{d} + \frac{5}{-d}$. Recall the mathematical procedure for adding rational expressions with opposite denominators by arranging the following steps in the correct order.

A HVAC technician is measuring the pressure differential between two points in a ventilation system. The pressure at the first point is modeled by $\frac{7}{d}$ psi, and the pressure at the second point is modeled by $\frac{5}{-d}$ psi. To find the total pressure, the technician must calculate the sum $\frac{7}{d} + \frac{5}{-d}$. Which of the following is the simplified form of this sum?

An HVAC technician is balancing the pressure in a ventilation system by adding the expressions $\frac{7}{d}$ and $\frac{5}{-d}$. True or False: To create a common denominator of $d$, the technician can multiply the second expression by $\frac{-1}{-1}$ to obtain $\frac{-5}{d}$.

A logistics coordinator is calculating the net throughput of a sorting facility. The inflow rate is modeled by $\frac{7}{d}$ units per minute, and the return rate is modeled by $\frac{5}{-d}$ units per minute. To find the total net rate, the coordinator must evaluate the sum $\frac{7}{d} + \frac{5}{-d}$. Match each mathematical expression with the specific role it plays in the standard procedure for solving this sum.

A logistics coordinator is analyzing two shipping routes. The cost factor for the first route is modeled as $\frac{7}{d}$ and the cost factor for the second route is modeled as $\frac{5}{-d}$, where $d$ represents the delivery window in days. To find the total cost factor, the coordinator must add these two expressions. Recognizing that the denominators are exact opposites, the coordinator recalls that they can create a common denominator by multiplying both the numerator and the denominator of the second fraction by ____.