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Select one: a. M = gm-mt 2(m1 + m2)9(m2 m1)te b. M =2(m1 + mz)g(m2 m1)t2 c M =2(m + m2 ) 2g(m2 m1)te d M =2(m1 + m...

Question

Select one: a. M = gm-mt 2(m1 + m2)9(m2 m1)te b. M =2(m1 + mz)g(m2 m1)t2 c M =2(m + m2 ) 2g(m2 m1)te d M =2(m1 + m

Select one: a. M = gm-mt 2(m1 + m2) 9(m2 m1)te b. M = 2(m1 + mz) g(m2 m1)t2 c M = 2(m + m2 ) 2 g(m2 m1)te d M = 2(m1 + m



Answers

Let $M(x)=(2 x-1) /(x-2)$ (a) Compute $M(7) \text { and then } M \|(7)]$ (b) Compute $(M \circ M)(x)$ (c) Compute $(M \circ M)(7),$ using the formula you obtained in part (b). Check that your answer agrees with that obtained in part (a).

Well not very fair. One of the given congruence is, is not always to based on if a congruent to be more. Um So let's check the first one. We have a squared Congruent to be squared more M. So here we can apply the law of congruence is that is if a congruent to be more M, then we can see that a race to the power of C is congruent to be raised to the power of C ma am. So therefore this is squared congruent to be square more. Em is true because you can see that the value of C equal to two here. So this is always true. Now let's do the second one. We have a plus B. Congruent to B plus M more to em. So let's verify if uh this has to be true than a plus m minus or B plus M Should be divisible by two M. So let's first simplify this. This is a plus m -7 -M. You can cancel this game and then we hope e minus B. Uh when we use this condition that is a congruent to be more M. This can be returned otherwise as a minus B is equal to K. M. Which means a minus B is divisible by Yeah, but so we only know that a minus B is divisible by em. We are not sure if a minus B irreducible boy. Um So this is not true. So you can say that this is not true. Well let's uh do the 3rd 1 here we have am congruent to be m more M squared. So first let's simplify this. This can be written as AM minus B. M. We just start to check if this is divisible by M square, so we can factor M. And when we do that we get sometimes of a -7. Notice that from the first human condition, that is if a congressman to be more M, this can otherwise Spirit. And as a minus B equal to K times of mrk some numbers. So therefore we can replace this a minus B as kate. I'm self employed, which means we have key M squared. So this A m minus B m s equal to K M squared. In other words, we can say that I am minus B. M is divisible bike m squared. So this is true. Therefore from this, uh, we say that the second one is not always true is the answer for this question.

Okay, So to solve a phone equation or Mr by factoring the denominators So if I do that, I'll have em over M plus two times M minus juan, plus em over M plus one times n minus one then for the last part. So the bottom is gonna factor into M plus two times m plus one. So now that I have my factors are my denominators factored l now I'm gonna need to create a common denominator someone I multiply my first part by m plus one over and pulse one. So I'm gonna have em times and plus one over the common denominator M plus two times m plus one times and minus one. Known for the second part No wonder Multiply top and bottom by m plus two. Then my denominator is gonna be the same with the 1st 1 So in plus two times and plus one times m minus one them for the last bar I'm gonna most by top and bottom by M minus one So in the bottom gonna have an plus two times M plus wine times m minus one. So now that I have common denominators, what I'm gonna do some would have multiplied by this common denominator. So that's just gonna leave me with the numerator. Someone have m times and plus one plus m times Impulse to is equal to, um, times m minus want when I want to disturb you So I'm gonna have m squared plus m plus m squared post to him is equal to m squared minus m So if I combine my leg terms on the laughed will have two m squared and I have m plus two AM So that's three m and then on my left hand side I have m squared minus m So if I bring my m square to the left hand side and I bring my negative i m and ad empty both sides, I'll have m squared. Plus for em is equal to zero. So now if I factor am out, I'll have em times and plus for is equal to zero. So this is gonna tell me that I'm musical to zero and I'm is equal to negative for so just one thing also that we have to plug these in and make sure that they work. So I have to put them into the original equation. And if we do so, we'll end up with the following I Equality is so we'll have that zero plus zero is equal to zero. The plugs the or into the original equation. We should know this is true. And if we put in negative, four will end up with the following negative 2/3 is equal to negative 2/3. So since both of these work and they're correct so we could say the M is equal to zero and em is equal to negative four.

All right, everybody here on problem number 14 were wanting to multiply these two rational expressions. Now, when you multiply two rational expressions, the first thing you want to do is see if you can factor anything. Can't factor anything here. Next thing you want to do is see if there's anything that's on top. That's also on bottom that you can cancel out. There's not here. It may look like a rhythm in minus two in the M Plus two, but the M and the negative, too, are a package deal, so it's got to be that whole thing on top. You'd also need a name minus two on bottom, but you don't have that you've done in plus two, so there's nothing you can cancel out, and so you just multiply straight across. So you take in minus two times M numbers. You don't leave. It is in minus two times AM, although I will change the order here just because that's what we normally do. And we write these relight the mono middle first, then the binomial, and then on the bottom you have in plus two times in minus one. There's no need to foil that out. We'll just leave it written like this, and so this is what we get

That these two are similar in that they both looked like a variable squared minus variable equals to someone with my two over here equals zero. And I see that this is indeed factory ble No one. I factor it. I get that the IHS equal to negative one or positive too. So no, I'm ready. Toe, Go take a look at what? My variable in the first equation is m squared minus one. So I m squared minus one equals negative one that care that one first. That's my easy one. So in this case, then m squared it was zero and taking the square root of both sides than M equals zero. My second option here is that get a different color M squared minus one equals two that tells me that I m squared equals three. Taking the square root of both sides m equals positive or negative square root at three. My be equation tells me my variable is m squared so I m squared equals negative. One tells me the m equals plus or minus. I I remember when I take the square root of both sides here, get the square root of negative one and that's equal toe I Okay, and then night or M squared equals two and again, taking the square root of both sides am equals plus or minus the square root of two.


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