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Write the partial fraction decomposition of the rational expression6x2 6x + 3...

Question

Write the partial fraction decomposition of the rational expression6x2 6x + 3

Write the partial fraction decomposition of the rational expression 6x2 6x + 3



Answers

Find the partial fraction decomposition of the rational function. $$ \frac{x+6}{x(x+3)} $$

Given exhibition is a crisp letter minus six x plus b divided by Explain this food for you. So living here could be composed in part protection for doing this really comported first by using unknown concert hooligans. I did see explain this school. Let's be X minus Google's Where plus C. I think my next group you now Our goal is to find a B and C for Bring this live in her mighty play X minus two for your group portside so it will get expire minus 6 63 Did I decide x minus to hold you in my life by explain this group for you, it is equal to a explain this school. Blessed be, it's minus group woods player. Let's see X minus group for you. Former divide by minus two or you but so even even get X squared minus six. Ecstasy equals a thanks minus Newport's quiet Les Bee X minus group bliss See further will get excess where minus six sexless equals two. A. It was when minus forex less four. Bless Me X minus ruthless excess where minus six express P It was to gain excess square minus four A. That's foreign. Bless the X minus B c. Now with the indictment, will get excess flying minus 66 State work School E X X Player minus four plus B x This What is my next movie? Pla's? Now they know Vincent seem. Then their patients are all the same, so we can buy a is equal to one minus four a plus B equals minus six and four. A minus movie. Let's see. It was the forget intuition. One question Immigration. By solving the sea, we will get. He wants to one V puts minus go and see if he first minus I and the patches. Action is fun. Divided by X minus two. My school divided by X minus. Do spire minus five, divided by X minus two for you, is it? I'm

So we're asked to find the partial fraction Bacall position. If you look at the denominator, the two times already factored and were distinct, so we can use case one. So it's what back you get a over X plus be over explosive. Three. Now we need to multiply bread a common denominator, which is X Times X plus three. You would see that all factions area extra exposed. Three Thanks Times X close three gets in counseling xxx explosively with history and what we're left with is export six. Is it could you a Times X plus three plus B names. Ex expanding the A that a x Hey, just 223 a plus B x. Okay, Now combining my terms, you get a plus B times X It was three a. Now let's build our system of equations. Let's look at our coefficients for X critical, efficient one and ankles. We're a bee is a good one And Marco efficient are constantly have a six manager ache. So we're three. A is equal to six. Okay, we can solve for a divided three on both sides of a executive now. So being too into seclusion one you got too close. Be Is you to one subject seal on both sides? No, it can't be. You go too. Negative one. Okay, so we have our coefficients A and B. It's rewrite it. You get two over X plus being which one over week? I don't know. Okay. Would have one over X plus three. And that is our partial fractions decomposition.

Rational expression Explode six upon x Q Negative three times X Esquire Negative four times eggs plus stroll. So in description, we have to write partial fraction decomposition off the rational expression. Now you can see that here in the denominator, we have to find the factor. So our factor is X plus e Ah, phone. The factor off denominator is X square Negative. Full time Xnegative three. So you can see that here. How we find it X cube. Negative. Three times X square, 94 Time X plus 12. So we make there and we take common here X square Onda, we get X 93 No, we attack DCF for Jews four. Then we get X negative three So you can see that our factor which is X squared. Negative negative four time X 93 Now we can factor more so you can see that here X square blue Negative four means we can apply the formula A Squire Negative be Squire. Cool Do e plus B time A minus feet. So we get eggs plus two time xnegative too. Time eggs. Negative three. Now we have to write form off decomposition So X plus six upon X plus two times X negative, too Time X negative three Equal toe airfone X plus two plus B upon xnegative too plus C upon xnegative three. Now we have to take least common denominator. So the right side then we get a time Xnegative to time Xnegative three less be time Ex father due to time Xnegative three Let's see X Negative Positive two times X Negative to now we substitute upon X plus two time X negative, too Time Xnegative three. Now we have to multiply both sides by X plus two times X Negative two times X negative three Then we get eggs Negative six Positive six Sorry. Equal to a time. Eggs negative too Time eggs Negative three Yes B x plus two time Xnegative three plus C time eggs positive too Time eggs Negative too. Now we put X equal to see you. Then we get eight equal to negative four times b so you can see that be equal toe negative too. Now we put execute toe tree Then we get we could do Sorry sequel to 9.5. Now we put execute negative too. Then we get for equal to 20 times e So we know that equal toe What Upon five. Now we put that value in the rational expression and we get X plus six upon X plus two time xnegative, too. Time xnegative tree equal toe one upon five time X plus two negative two times Sorry to upon X negative too Plus nine upon five time X 93. So it is all final answer.

A rational exhibition three times eggs plus six upon X Q plus two times x So in discussion, we have to write partial fraction decomposition off the rational expression. So here you can see that the degree off denominator is greater than to the degree off numerator. So we have to find the factor off denominator and alright form off decomposition so you can see that here three times X plus six upon eggs time Axis choir plus two equal toe. Now we have great for more decomposition. So here is aquatic form and here is exponential. So you can write like that A upon X lose for the acquiring form. You know that the time Eggs plus C upon axis Quiet plus two. Now we have to take least common denominator and we get X time. Axis Choir Plus two and New Monitor is a time Axis choir plus two plus be time X plus e time X. Now we help multiply both sides by X time X square, plus two. Then we get three times eggs plus six equal to E X square, plus two times e less Be time Axis choir close. See Time X So we can combine like terms. So here, e plus B time X square plus See time eggs plus two time. Yeah, Now quitting the coefficients off like drones and we get e plus me equal to see you sequel Do three and constant room two times a equal toe sick so you can see that here Equal Do three sequel Toe three and be equal Do Negative three. So now we put that value in this equation and we get three time eggs plus six upon X time X choir plus two equal toe three upon eggs. Words negative three times eggs blows three a bone access square plus two. After that, we find a graph for this expression so you can see that here our growth for this expression and or filings. Where is three upon eggs plus negative three times X plus three upon X square, plus two


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