Perform each division. See Examples 7 and 8. (-4m^2n^2-21mn^3+18m...

Question

Perform each division. See Examples 7 and 8. (-4m^2n^2-21mn^3+18mn^2)/(-14m^2n^3)

Accepted Answer

Hey everyone in this problem we are asked to simplify by completely dividing the following expression. And the expression were given is negative six G squared H cubed minus nine G. H cubed plus 12 G H squared divided by negative 15 G squared H cubed. Okay so let's just go ahead and rewrite what we're given minus nine G. H. Cute plus 12 G. H squared. And just watch your exponents when you're rewriting the expression, you're not mixing anything up because it's gonna change your answer. Negative 15 G squared H cubed. Alright so when we're giving an expression like this were asked to simplify what we'll notice is that in the numerator we have three separate terms that are either added or subtracted. Okay over a common denominator what we can do is we can separate this expression out and then we'll be able to simplify kind of term by term. So what do I mean? Well we have negative six G squared H cubed divided by negative 15 G squared H. Cute minus nine G. H cubed divided by negative 15 G squared H. Q. A. Plus 12 G. H squared divided by negative 15 G squared H. Q. Okay and again because we have the terms in the numerator added or subtracted and were divided by a common denominator. We can break these up into these three terms. Okay if the terms in the numerator are multiplied together, we wouldn't be able to do this like this. Okay. Alright and we have just a single kind of term in the denominator being multiplied. So we we don't need to find kind of linear factors or anything like that. Alright so working term by term. Okay we can start with the Constant. We have negative six divided by -15. That's going to become positive. So we get six divided by 15. Now we have G squared divided by G squared. Okay when we have the same base and we divide the exponents subtract. So we get G to the two minus two. Okay. And you might notice that the g squared kind of divides out? Um And same with the H. H three minus three and you might notice G squared H. Q. G squared H cube. They divide out. We're left with just one. Okay, I'm just showing you in case you didn't realize that or in case the numbers work out differently how you would approach this K. We subtract the exponents and again you'll get G to the zero H. Zero which is going to give you that one that you would get if you just realized right away that those divide out. Alright. Next term negative nine divided by negative 15. That's gonna give us a positive 9/15 and we'll simplify these fractions in the next step. Okay. Alright. G. Okay. In the numerator we have exponent one in the denominator of exponent two. So we have one minus two. Okay you always subtract the exponent in the numerator minus the exponent of the denominator And then the H 3 -3. All right now in this last room we have positive 12 divided by negative 15. So we're gonna get negative. Well over 15 G. To the exponent one minus two and H. Two. The exponent two minus three. Alright so next step we're gonna simplify what we've written down here. So we have six. We have 15. Okay you'll notice that these both divide by three? Yes so we divide by three. We can write this as 2/5 G. To the two minus two gives us G. To the zero which is one. H. To the three minus three gives us each to the zero which is one. And so we have just 2/5 for this term. 9/5 again they both divide by three. If we divide by three we get 3/5 G. to the 1 -2 gives us G to the negative one and H. Two the three minus three H. To the zero which gives us one as we're done with that term. And then 12/15. Again we can divide by three, we're going to get negative 4/5 G. To the negative one and then we have reached the negative one as well. Alright so this is mostly simplified we're just going to rewrite this to kind of match the format of our answer choices. Um When we have negative exponents remember that we can write them in the denominator and they're going to be positive exponents there so we can write G to the -1 as one over G. Okay, so we get 3/5 G. And same thing here, we get 4/5 G. H. For that last term. All right. So the simplified version of our original expression is going to be to over five plus 3/5 G minus 4/5 G. H. And that is going to correspond with answer. C. Thanks everyone for watching. I hope this video helped see you in the next one.

Perform each division. See Examples 7 and 8. (-4m^2n^2-21mn^3+18mn^2)/(-14m^2n^3)

Key Concepts

Polynomial Division

Simplifying Rational Expressions

Negative Exponents