Perform each division. See Examples 7 and 8. (8wxy^2+3wx^2y+12w^2...

Question

Perform each division. See Examples 7 and 8. (8wxy^2+3wx^2y+12w^2xy)/(4wx^2y)

Accepted Answer

Hey everyone welcome back in this problem we are asked to simplify by completely dividing the following expression expression we're given is 12 J squared G squared H cubed plus five J squared G cubed H squared plus 15 J cube G squared H squared. All divided by three J squared G cubed H squared. Okay, so let's just go ahead and rewrite this. Um So we can see what we're trying to do. 12 J squared G squared H cubed. And just be careful when you're rewriting the problem that you don't mix up any of the exponents. Okay. It can be really easy to mix up a two or three when you're rewriting the problem and that's going to change your answer. All right. All divided by three J Squared G. Okay so we have a problem like this, we have kind of three things. Three terms added together in the numerator. All divided by this one denominator. What we can do is we can split those up if we split those up we'll have smaller problems to deal with um and they'll be easier to manage. Okay so we get 12 J squared G squared H cubed divided by three J squared G cubed H squared plus. Okay, so we're just breaking up each term and we can do this because we're adding. Okay and we have this common denominator here. If you have terms multiplied together in the numerator, you cannot split them up like this. You would need to kind of factor them out um And deal with them more together than being able to split them up like this. So because we have these terms added together with a common denominator we can break them out like this three J squared G cubed H squared. And this last term 15 J cube G squared H squared, divided by three J squared G cubed H squared. Alright so now we can deal with these one at a time. Alright so when we're looking at these the first thing we can do is divide the numbers. Okay so in this first term we're gonna have 12 divided by three. That's gonna give us four and then we're gonna look at each of these variables together. We have J squared divided by J squared when we divide Terms with exponents. Okay we have the same base and they have an exponent we subtract the exponents. So this is gonna be J to the exponent 2 -2. Okay then we get G. And again subtract the exponents 2 - And H Exponent 3 -2. Okay so this is for our first term we have our second term and in this term we're gonna have 5/3 we'll leave it like that because we can't simplify that. Okay we get J and again 2 -2. G 3 -3 an H two minus two. Okay and you may have noticed right off the bat here in the numerator and the denominator of this term. We have j squared G cubed H squared for both of them. So those will all divide out and you're just gonna get one. So this is gonna be five thirds. Okay But I do want to show this process of subtracting those exponents. Um So that if it doesn't work out perfectly you know how to deal with this. Okay all of these exponents will be zero. Um So this will all go to one. Alright so 15 divided by three is gonna give us five. We get J. Three minus two G. To minus three and H. Two minus two. All right so now we're just left to simplify. Okay so we have four J. T. Exponent two minus two. Well that's gonna be J. T. The exponents zero that's just gonna be one. Okay we get G. To the two minus three. That's gonna be G. To the negative one and then H. Three minus two is going to be a church. This middle term. We talked about already all of these exponents are gonna be zero. So we're going to get just one. So we have five thirds. They're just a constant. And then this final term we have five J. Okay three minutes to gives us once we get J. G. To the negative one and then we have a choice to the zero which is gonna be one. Now these exponents of -1. Remember we can write those as exponents of one in the denominator. So we can write this as four H. Over G. Plus five thirds plus five J. Over G. Okay. And that's gonna be our simplified version of the original expression we were given. Okay we have four H. Over G. Plus five thirds plus five J. Over G. And if we compare that to our answers it's gonna be answer choice B. Thanks everyone for watching. I hope this video helped see you in the next one.

Perform each division. See Examples 7 and 8. (8wxy^2+3wx^2y+12w^2xy)/(4wx^2y)

Key Concepts

Polynomial Division

Factoring Out Common Terms

Simplifying Rational Expressions