SOLUTION: Could you please help me solve this equation? 2x^2-x-9/(x+1)(x^2+5)=A/x+1+Bx+C/x^2+5

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Question 151164: Could you please help me solve this equation?
2x^2-x-9/(x+1)(x^2+5)=A/x+1+Bx+C/x^2+5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given equation.


Multiply every term by the LCD %28x%2B1%29%28x%5E2%2B5%29. This will cancel out the denominators.


2x%5E2-x-9=A%28x%5E2%2B5%29%2B%28x%2B1%29%28Bx%2BC%29 Multiply and simplify.


2x%5E2-x-9=A%28x%5E2%2B5%29%2BBx%5E2%2BCx%2BBx%2BC FOIL


2x%5E2-x-9=Ax%5E2%2B5A%2BBx%5E2%2BCx%2BBx%2BC Distribute



Take note that the x%5E2 terms on the right side are Ax%5E2 and Bx%5E2. So this means that 2x%5E2=Ax%5E2%2BBx%5E2 and 2=A%2BB. So the first equation is A%2BB=2


Also, notice how the x terms on the right side are Bx and Cx. So this means that -x=Bx%2BCx and 2=B%2BC. So the second equation is B%2BC=-1


Finally, notice how the constant terms on the right side are 5A and C. So this means that -9=5A%2BC. So the third equation is 5A%2BC=-9

A%2BB=2 Start with the first equation.


A=2-B Subtract B from both sides.


5A%2BC=-9 Move onto the third equation


5%282-B%29%2BC=-9 Plug in A=2-B


10-5B%2BC=-9 Distribute


-5B%2BC=-19 Subtract 10 from both sides.


So we now have the system of equations

system%28B%2BC=-1%2C-5B%2BC=-19%29


Use any method to solve the system, to get the solutions:

B=3 and C=-4


A=2-B Start with the given equation.


A=2-3 Plug in B=3


A=-1 Subtract




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Answer:

So the answers are

A=-1, B=3, and C=-4


Which means that





Note: to check your answer, graph the left side and the right side. The two functions should be the same graph.