SOLUTION: Could you please help me solve this equation for A, B, and C. 11x^2-x+8/(x+1)(X^2+4)=A/(x+1)+Bx+C/X^2+4

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Could you please help me solve this equation for A, B, and C. 11x^2-x+8/(x+1)(X^2+4)=A/(x+1)+Bx+C/X^2+4      Log On


   

Question 151438: Could you please help me solve this equation for A, B, and C.
11x^2-x+8/(x+1)(X^2+4)=A/(x+1)+Bx+C/X^2+4
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%2B4%29 to clear the fractions.


11x%5E2-x%2B8=%28x%5E2%2B4%29%28A%29%2B%28x%2B1%29%28Bx%2BC%29 Simplify


11x%5E2-x%2B8=A%28x%5E2%2B4%29%2B%28x%2B1%29%28Bx%2BC%29 Rearrange the terms


11x%5E2-x%2B8=A%28x%5E2%2B4%29%2BBx%5E2%2BCx%2BBx%2BC FOIL


11x%5E2-x%2B8=Ax%5E2%2B4A%2BBx%5E2%2BCx%2BBx%2BC Distribute





Notice how the x%5E2 terms on the right side are Ax%5E2 and Bx%5E2. So this means that Ax%5E2%2BBx%5E2=11x%5E2 and A%2BB=11


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

Finally, the constant terms on the right side are 4A and C. So this means that 4A%2BC=8



A%2BB=11 Start with the first equation.


B=11-A Subtract A from both sides.


B%2BC=-1 Move onto the second equation


11-A%2BC=-1 Plug in B=11-A


-A%2BC=-12 Subtract 11 from both sides.


-4A%2B4C=-48 Multiply both sides by 4.


Add this equation to equation #3

-4A%2B4C=-48
+4A%2BC=8
--------------
0A%2B5C=-40


5C=-40 Simplify


C=-8 Divide both sides by 5.


4A%2BC=8 Go back to the third equation


4A-8=8 Plug in C=-8


4A=16 Add 8 to both sides.


A=4 Divide both sides by 4.


B=11-A Move onto the first isolated equation


B=11-4 Plug in A=4


B=7 Subtract


====================================================

So the value of the constants are

A=4, B=7, and C=-8


So this means that the equation is