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In dividing polynomials $$2$\frac{P}{Q} \div \frac{R}{S}$$ why is it necessary to state that polynomial $R$ is not equal to $0 ?$

Okay, so for this question were asked the fact that by grouping, looking at our 1st 2 times, we see that we haven't are in common. So let's fact that out To get a r Times p minus two and then for our last two terms, we have an A in common Sophie factor that out we get negative, Pete plus two. So we see that native peoples to and P minus two are opposites of each other. So we contract out of negative one from negative p for us, too, to get t minus still. So if we did, I would get native a times p minus two and then we get our times p minutes to hear. Now we see that we have a P minus student common that week. In fact, they're out. So if you factor that out, we get P minus. Two times are minus a

So we're gonna factor these two very first thing we want to do a star by grouping. We're gonna group her 1st 2 terms together. We're in a group for the last two times together, making sure that we keep this sign with our terms. So I'm just gonna put a plus sign in between them. So, given that I'm gonna take the g c f out of my 1st 2 which would be C when I factor old Z, I would get Z squared divided by Z, which leaves me with Z and I get tensy divided by sea. Which leaves me with 10. When I do this the second I want to make sure that I keep this sign so it's gonna be a negative. And then they both have in common and negative seven. So I have negative seven and then divide that into negative seven z. That leaves me with Z Divide negative 70 by negative seven. And I get positive. 10. For this to work your soup parentheses need to be the same, and they will be one of your factors. The terms on the outside. Well, make up your other factor and it doesn't matter which order you write these factors in because if you were to multiply and give animal play out to be the same, just be very careful with the signs.

Problem. 69 negative 3/8 R squared plus 2/9 are plus one third minus the quantity Negative 7/16 R squared minus 5/9 R plus 7/6. So what we dio for the subtraction is we distribute this negative sign to all of three of those places and then copied on the first polynomial and then distributed. Now we can combine like terms, so this one ends up being 1/16 r squared. Then we have our our terms. So that's 7/9 are and we have one third minus 76 Just negative 5/6. This is our answer.

In this cushion, it is given that three double square minus 12 divided by double squared plus five W plus six in the numerator. We can take three common here. Inside bracket. It'll be doubly square minus four, divided by they're denominator. Recon factories were splitting the middle term so we can write it as double square plus studio blue plus treat a blue plus six now in the numerator that the Blue Square minus four, it can very 10 US W Square minus two squared in the denominator from the first to Tom Double Square, Prostitute of We Can Take the Blue Common and said Racket, It'll Bitter Blue Plus two plus from the second to Tum, we can take three common in said Bracket. Little Bit of Blue plus two. The numerator. We can write it as double square minus two whole square. This one can wear it and asked the blue plus two times the blue minus two. Divided by it will be the blue plus two times W plus tree. Now we can see that from the numerator and denominator. The blue plus two and W plus two will get cancelled so we can write the expression us three times The blue minus two divided away. The blue plus three