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Divide. $$ \frac{2 n^{2}-5 n-3}{4 n^{2}-12 n-7} \div \frac{4 n+5}{2 n-7} $$
To solve this problem, I can write to given express and as 7 90 square minus 14 and by 8 10 multiplication four and plus 24th by any square plus four and minus two world solving it further I get the value is seven and multiplication and minus two by 8. 10 multiplication food and plus six bye and plus six multiplication and minus two. Solving it further and canceling this symptom. So this term and disturbing get canceled this term this term Get canceled this become one and this becomes toe and descend Descend get canceled So the final equation become so just look at it carefully The final question becomes seven by two which is a bird answer for this problem.
Once. Yeah. How about it? This one of what? Uh, just what I have. Well, what This six? This, uh that's this. So I have fine with out of no. On this six. I have I Mr, you know, not a
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.
What's the problem is in squared months. Five. Impulse four. Divided by a minus four. No, everything's in greatest to lowest degree, so we can go ahead and write it. It's a long division problem right off the bat. We don't have toe rearrange or anything. Now end times in is n squared. So right that and then negative four times in lots. Negative for N. Prince Sees Attracted sign Make sure to always put Prince sees destroyed the negative to both terms. So we had n squared minus and squared with zero negative five minus and negative for in just the same as negative five plus foreign or negative in Bring Down the positive for the Net. The positive end times negative one would be a negative and and negative one time *** four's a positive for Princz attraction. Sign negative in minus and negative, and it's sames negative in plus end or zero Positive for minus four is also zero. So we're done and if you want to, a real quick check. One way I could tell us is true is that if I write out in squared in squared minus five in plus four well factors of four that add to negative five are negative one and negative for because negative one time thing and force positive for a negative one plus negative force. Negative five. And so, by this trick, I know that in squared minus five in plus four can actually be written as in plus four our whips up steps in minus four times in minus one, which the n minus one is the solution we got. And what was our divisor while our divisor was in minus four? So I see that this indeed true.