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Exercise 5.1; Solve the Following FMTh relations with ( I6_1 3bn 2" wich 61 Ad 62ExerciseUse geuerating functicls wke...

Question

Exercise 5.1; Solve the Following FMTh relations with ( I6_1 3bn 2" wich 61 Ad 62ExerciseUse geuerating functicls wke

Exercise 5.1; Solve the Following FMTh relations with ( I6_1 3bn 2" wich 61 Ad 62 Exercise Use geuerating functicls wke



Answers

For the following exercises, determine whether the relation is a function.
$(5,2),(6,1),(6,2),(4,8) $

For the given problem, we want to minimize production costs. Bye. Uh Resolving exercise 52 Bring back Texas sized 52. We end up seeing that we can take this cost function and then consider um dysfunction right here. Yeah, we can get rid of this now and then. We can also consider C. Prime of X. So what we end up seeing is that this function here is going to equal the average cost function. So I will consider cfx writing by X. What we end up getting is that these two functions are going to eventually equal each other and that's going to show us the same exact result for the average cost. So that's our final answer.

We have an expression here that has the common denominator, and we're subtracting. It's too rational expressions and we have our common denominator, which is a minus five, and that will stay consistent in our solution because only subtract fractions will keep the common denominator. But we do need to subject the new Marine years so 10 minus I would give me five. This is an acceptable solution. Another option of how you could write this is because split it into two different factions so we could write it as five over a minus. Viable were five and 5/5 simple kinds. The one so another way we could write our solution five divided by a minus one either of these

We have an example here to subtract two rational expression, and they both have a don't denominator in common of a minor. Now, on the ADDers of track fractions, we need to make sure we have a common denominator. So we already do have that. So I know my solution is gonna have that same common denominator. And then in the numerator, we have 10 minus five, which would simplify five. So this would be our final solution, because I noticed there's nothing that

From this example were given three different pieces toe Adan subtract together and so some three of some fractions involved. Our first step is to make sure that we have a common denominator before we can do anything else. But we're going to do is the two terms that we have fractions with. We're gonna factor the denominators, see what our common denominator should be. I'm gonna rewrite the five Justice 5/1, so we keep it. Infraction notation three X minus six. They will have a three and Commons weaken. Factor out the three and divide each of those by three to get X minus two and our second fraction here. They both have an exit in common, so we could factor out the X can rewrite that as extend that quantity X minus two. So therefore, looking at all the unique pieces in the denominator, it looks like our common to nominee. There should be three find x times the quantity X minus two. So I took the three d x minus two on the X the X minus two. They just both have in common. So this should be our comment in a meter in order to get that common denominator, we need to multiply each fraction by whatever pieces in this thing to make it a common denominator. So, for example, in this first reaction, I don't have anything in the dumb. Very just have that one. So I need the multiply by the entire I need to multiply by the entire common denominator, which is three x times the quantity X minus two and whatever we multiplied by on top, we also have to multiply by all bottom. We want to do both so that we have an equivalent fraction this middle fraction for missing the X. We have the three and the X minus two, but not the X. We're gonna multiply the denominator by ex to make it look like the common denominator, which means we all assembled by the top by it. And then in our last traction, we have the X and the exposed to, but we're missing the three. So we're gonna mult by the bottom by three and the top by three. Those them both eyeing each of these fractions the first fraction I have to multiply five times the re X X minus two That's going to give us the numerator of 50 next times the quantity X minus two. On the denominator is three x times the quantity X minus two. Hey, that looks way more complicated, but it's gonna be helpful because we know of a common denominator our second fraction that we're subtracting. We now have that common denominator and the numerator one times x is X and the third fraction we have the common denominator and the top we have three times three, which is mine for the first fraction, we could use distributive property to simplify this further. So this is the same 50 next times access 15 x squared and 50 Next. My times name too is negative. 30. So we can rewrite this as 15 x squared minus 30 whom 30 X So from here we can combine like terms. So my 1st 1 I had, uh my 15 x squared minus 30 x my second when I have minus X and my third fraction of my numerator have plus nine. So we combine our like terms here Negative 30 x minus One more x is negative. 31 x sore numerator would become 15 x squared minus 31 X plus nine when our denominator would be our common denominator. Three x times the quantity X minus two And since we don't have a way to simplify this any further, this would be


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