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To calculate the volume of a chemical produced in a day a chemical manufacturing company uses the following formula below: V(x)=[C₁​(x)+C₂​(x)](H(x)) expression for the holding container with respect to the number of units produced. The equations for the the the chith produced are given below: C₁​(x)=x/x+1​,C₂​(x)=2/x−3​ The equation for the holding container with respect to the number of unit produced is given below: H(x)=x/x³−9x​ What rational expression C(x) do you get when you combine the two chemicals?

Answer :

Final Answer:

The rational expression C(x) that represents the combined chemical produced by the manufacturing company is C(x) = [(x/(x+1)) + (2/(x-3))] * (x/(x³-9x)).

Explanation:

To find the rational expression C(x) representing the combined chemicals, we first combine the expressions for C₁(x) and C₂(x) into a single expression:

C₁(x) = x / (x+1)

C₂(x) = 2 / (x-3)

Now, we need to multiply these two expressions by the holding container expression H(x):

H(x) = x / (x³-9x)

So, C(x) = [C₁(x) + C₂(x)] * H(x)

Substitute the values of C₁(x), C₂(x), and H(x) into the expression:

C(x) = [(x/(x+1)) + (2/(x-3))] * (x/(x³-9x))

This is the rational expression that represents the combined chemical produced by the company as a function of the number of units produced, x.

Understanding how to combine rational expressions is essential in chemical manufacturing, as it helps in optimizing production processes and ensuring the right chemical composition for various products.

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