A clothing company uses the expressions that follow to estimate revenue and expenses based on the production of x lots of clothes:
Revenue:
Expenses:
The ratio of revenue to expenses is represented by the rational expression that follows:
A. Factor the numerator and denominator out of the rational expression, and simplify
To factor the numerator and denominator out of the rational expression, we need to first identify the expressions for revenue and expenses.
Given that the clothing company estimates revenue and expenses based on the production of x lots of clothes, we can assume that both revenue and expenses are linear functions of x.
Let's say the expression for revenue is R(x) and the expression for expenses is E(x).
Now, let's write the rational expression for the ratio of revenue to expenses:
Ratio = Revenue/Expenses = R(x) / E(x)
To factor the numerator and denominator out of the rational expression, we need to find any common factors.
For example, if the expression for revenue is R(x) = 3x + 1 and the expression for expenses is E(x) = 2x - 5, we can see that there are no common factors between the numerator and denominator. So, we cannot factor them out.
However, if the expressions for revenue and expenses have common factors, you can simplify the rational expression by factoring out those common factors.
Once the common factors are factored out, you can simplify the rational expression further by canceling out any common factors present in both the numerator and denominator.
In summary, to factor the numerator and denominator out of the rational expression and simplify it, you need to identify the expressions for revenue and expenses, find any common factors, factor them out, and then cancel out any common factors between the numerator and denominator.