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Use the division algorithm to rewrite each improper rational expression as the sum of a polynomial and a proper rational expression. Find the partial fraction decom...

Question

Use the division algorithm to rewrite each improper rational expression as the sum of a polynomial and a proper rational expression. Find the partial fraction decomposition of the proper rational expression. Finally, express the improper rational expression as the sum of a polynomial and the partial fraction decomposition.$$ rac{x^{3}-3 x^{2}+1}{x^{2}+5 x+6}$$

Use the division algorithm to rewrite each improper rational expression as the sum of a polynomial and a proper rational expression. Find the partial fraction decomposition of the proper rational expression. Finally, express the improper rational expression as the sum of a polynomial and the partial fraction decomposition. $$ \frac{x^{3}-3 x^{2}+1}{x^{2}+5 x+6} $$



Answers

Find the partial fraction decomposition of each rational expression. $$ \frac{x^{2}+1}{x^{3}+x^{2}-5 x+3} $$

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Given expression is I think this lead minus six Explosive in divided by X minus one X x squared plus one. We need to be completed and back protection for doing this. We didn't know Constant. So a by explain this one less the ecstasy bite. It's a slam less one. Now our fullest opine gave Ian see. For doing this, we will multiply X minus one x squared +12 Both site so five exist by a nine at six explosive in divided by X minus one X squared plus one My big legs I X minus one x x squared plus one equals true. Okay, divide by X minus one less Be explicit. E divide back to square less one. What might ignite by? Explain this one exist. Quietness when never is already we will get by Victor Square minus six. Explosive in equals Do a X squared plus one plus b x plus e x minus one given told with we would get five pixels square minus six explosive and equals two. A excess Where Let's a les bee. It's a square minus B x. Let's see, it's minus T No. Five ixis player minus 66 Let's see even equal stoop a blessed be exist with less minus B plus C eggs. Bless K minus C. Now, if nobody knows that same, then that coefficients are also same. It was equal to fight minus B, but a sequel to minus six a minus is equal to seven. We'll be questionable ones. Question number. Do any question number the best living these missions ever. Get eight with stoop. Okay, be going toe and sequel do minus wolf. Hence the March election is C by. Explain this one less Who? X minus war by excess Wear this one. That is this answer.

Given expression is by faith is quiet plus six x plus three divided by explicit Lynn excess. Where plus two X plus two. We need to be composite in March. Direction For doing this, we've been righted using a nonsense, so it is equal to a divide by X plus one. Bless, be explicit, divided by exit square bliss to explore this do now Our goal is to find a B and C for doing this. We will multiply, explains one Exit Square District Class Toto board side. So they will get I think this way. 66 Last three divided by X plus one X squared plus two x plus two multiplied by express line x x squared plus two x plus Don't equitable Hey, the ride by explosive on Let's Be Explicit, divided by It's a Squared plus two x plus toe. All my good, played by X plus line Exit Square plus two X Place. Don't Living Solar Rick Really get five fixes Squared Bless 66 plus three equals two e X square plus to express toe less. Be explicit. E X plus one. You've been sold weekly will get I picked the square Bless X X plus three equal a X squared plus two x Let's do a blessed be x a square. Blessed be X Bless C X bless. See now we were really injured. The building five x a square plus six six plus three equals two a plus B X squared to a plus B plus C X plus two a plus C. Now I have to pretty normal science team and their confusions are also seem so. A plus. B equals +05 to a plus D plus C equals +06 and to a policy equal do three. What really questionable one. Question Number two. Any question Number three. By solving these three questions, we will get a equal stoop. You'll be quick to three and sequel toe minus one. Hence, the partial direction is to divide by X plus one. Bless the X minus one Divide by X Square. Plus to express do it is the answer

Given expression is six x a square mine ethics plus one divide by x Q. Less excess Where No sex Pless, we need to be comported partial attraction for doing this for us women. Fact that I have a nominee after factoring middle May. Then we will get six sixes square minus X plus one. Divide by express. One. Excess weirdness you know, not really the known constant, so it didn't equals two. Yeah, divide by X plus one. Let's be explicit. Si divide by excess quietness. But now bullets to find a BNC for doing this with my life. A plus one f x squared plus one group Both say so. We will get six sectors where my next plus one divide by X plus one a crisp led, most one murdered night by explodes when X squared plus one equals two. A divide by X plus one plus B x Plessy Divide by X squared plus one Well, my deployed by express one excess quietness. One. After solving it, we will get xxx where minus X plus one equals two a x x squared plus one. Let's be explicit. Si X plus one. Now we're furthers always. We will get six x squared minus six. That's when he goes to it. Was gladness e blessed be X this wire less v X. Let's see explicit see? No, we've been really will get six x squared minus X plus one equals two a plus B X square yes, B plus C x less witness. Not a coupon normal. Same in their computer. Charles was in tow. A plus B equals +26 b plus c with too much on this one, and it lets see both. Stoop. One would be the question about one question. Number two Elocution number. Hey, my solving these situations, we will get equals before the equal still do and C equals two minus three and the part reflection is full. Divide by x last month plus four x minus. Lee. Divide by excess supply of less one, and we will give the budget action off the given expedition


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