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6rMO 83OMeHoHOOMe...

Question

6rMO 83OMeHoHOOMe

6r MO 8 3 OMe Ho HO OMe



Answers

Divide. $$\frac{\frac{16 r+24}{r^{3}}}{\frac{12 r+18}{r}}$$

To clear the denominators. We're gonna multiply everything by our times. Ar minus one. Here. The ours would cancel out here, the AR minus ones would cancel out. All right, so eight times ar minus one. That's eight R minus eight. Three times our is three are and we're here. Three are times our minds. One is three r squared, minus three are So we got a quadratic equation. Uh, let's solve it. Well, let's get zeros on one side of this equation. It's gonna take us a couple steps, actually, eight R plus three hours, 11 are. All right. So now let's subtract. 11 are from both sides. Negative three R minus 11 R is negative. 14 are and will add eight to both sides. All right, zero cause three R squared minus 14 R plus eight. Let's use the quadratic formula to solve this so r equals negative. B Absolute Made 14 is 14 plus or minus the square root of B squared 14 squared, which is 1 96 minus four times a time. See a time C three times eight is 24 and four times 24 is 96 of minus 96. All over two times 80 times three is six. All right, so 14 plus or minus. The square root of 100 which is 10 all over six 14 minus 10 is four and 14 plus 10 is 24 so X could be or not are but are not expert are could be 2/3 or four 2/3 and for those of solutions to our equation.

According to the question we have given Equation is our square plus 16 is equal. Do it are first of all be rearing this equation. We have our square miners. It are plus 16 is equal to zero. And then the expanded the question we have our scwill minus four R minus four R plus 16 is equal to zero. And then we take common when they come and we have R minus four. And in this side with a common minus four, we have AR minus four is equal to zero. The factor comes out, there is our miners For an R minus four, we can say that there is r minus four. Hold care is a 20 the value of our calms our dairies for

In this problem. We're going to solve the absolute value equation because we have to isolate the absolute value and then solve by setting equal to both and negative two minus eight minus a. We'll have ar minus three. Value equals zero. Since it equals zero, there's only one solution. We can set this equal zero and add three to both sides to get r equals three. This is the only solution.

Okay, so we see that we have to and and are in common. So let's factor that out. So the fact that the two are well off of 16 divided by two, which is eight, aren't too far after day minus 1 28 part but two with just 64. And it s cute. Now we know that are is a perfect cute that's just equal to two to the power of three. And 64 is also a perfect cube. It's equal to 44 3 So we get the full one, and then we could be right that as or we could remind that into two are about three minus for us to depart three. And we know of axe. Um, this is in the form of the sun or the difference of two cubes so we can rewrite that or fact it out into the fallen. Get to our minus for s times that you are squared, which is four r squared close to our times for us, which is eight Rs and then plus for a squared, which is 16. That's squared


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