5

L1o{an+lbn n > 1,n = 24}...

Question

L1o{an+lbn n > 1,n = 24}

L1o {an+lbn n > 1,n = 24}



Answers

$$ \frac{n}{n+2}=\frac{8}{n^{2}-4}+3 $$

In this particular case, we have got and won the this dance medium and do is read it then and the one and three East credit than and two in this party to their case, The reflection over here is first slipped. Transmission is not and transmission is not so we have our way number one Andrea number three So far. Now the reflection over here from the second surface with make the face sleep So this will have fast slipped. So that's number two. Now, if this is reflected than the first gets flipped again and the transmission, the first gets flipped again. So just by looking at this, I can say that if the optical path lent equals integrates multiple off where event, then one to we're and three full, both with constructive the interfere if dare to l equals integral mas with us halfway event, then one and do and three verses. Four. They will destructive the ender. Fear

So solve this equation. Here we are going to multiply both sides by the LCD so we can see that the LCD is equal tow n plus one times and plus seven. So that means we're going to multiply on my side by the LCD. We're also going to multiply the right side by the LCD. Now we end up with and kinds on plus seven on the left side, and the right side is going to be six times and plus one fact distributing that will give us and square plus seven and is equal to six on six. Move everything over in the left side. Now we get unscored plus on minus six is equal to zero, so that can be factored into unplugged three times on minus two. So that gives us and it's equal to make it a three or a sequel. Now we can see that neither of those answers will give us a zero that are denominator. So which means both of them should be good answers you can. We'll go back into the original equation to check. So for friend is equal to negative three. That gives us negative three over negative three plus one is equal to six over, maybe 23%. So the left side is going to be negative. Three over. Thank you, too. And then the right side is going to be, um, six over for it's so this last seven cups positive through, over to, and the right side is also there over to once we simple. So that's good. You know, we check any clothes, too. That'll be to over two plus one, and that's six over to plus up. So this is true. Over three is equal to six overnight, which is true because six overnight simplifies to Children.

Equation to solve here is end to the power file over to equals thirty two Now end to the power five over two can actually. Burton as end to the power one half to the power five. So hand our half to the power five. So if I do that, then I have n our half to the power Fi And then I started thinking, Hey, how can I third right thirty two as a power of five. So if you remember to to the fifth power is actually equal to thirty two. So I can replace the thirty two by two to the fifth power. When the exponents are same, then the bases are also same. So we got into the power one half it goes to or in other words, what you're saying is that the square root off and is too. Now what number has to as it squared that could be for or conversely, I can say, hey, busted up was the worst operation to square the inverse operation to square two square. So I have n equals two squared, which is equal to four. So my answer for this question would be and equals four

So in this problem we are. We are We are dividing with variables that have coefficients and ex ones. And so we're gonna use to rules here. So our first rule basically states that if we have terms that are added or subtracted in the numerator and we divide by some value, well, we can split them up. So we have x divided by C plus or minus. Why by bicycle. So let's let's do that. Let's go ahead and and split up our numerator. So we have we have 24 and to the eighth over negative six and square. So this is subtracted with 12 and 12 and to be 5 12 into the fifth over negative six and square. So plus we have 30 and cute over negative six and square. So what we're gonna do is we're gonna work on the coefficients for so we have 24 divided by negative six. Let's get a four. We have end to the eight divide by and square And so remember that when we're dividing very bulls with exponents, what we have If we have X to the a divided by X to the B, we're left with X to the A minus bi. And so this is rule to and so end to the A Divide by N squared gives us end to the A minus two. Well, that is and to be 68 minus two or six. So this is minus. This is my ass. And then we have 12 divided by negative six. This gives us a negative, too. And we have end to the fifth, divided by and square. So if we have entered 50 but by and squared well, what we're left with is and 25 minus two so and to the five months to which is and cute and so we can simplify this a little bit. So if we have a minus and negative, we know that should be This should be positive. We have positive, entered five months to other end. Cute. And so now we have a plus 30. Divided by a negative. Six is negative. Five, we have minus five minus five, and to the three minus two. Entered the three months choose into the one. And if we have a variable just and we know that there's an exhumed assumed exponents of one, So this is our final solution. So we used our first term to split up the numerator, and we used our second rule to to figure out how we should divide variables with exponents. And so what we're left with is negative for and to the sixth plus plus, this would be to plus two and cute plus two n cubed minus five n. So this is our final solution.


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