SOLUTION: Since there is no section for partial equations, I will put the question here. (x^2 -x -21)/(2x^3-x^2+8x-4) Thank you, Alexus

Algebra ->  Equations -> SOLUTION: Since there is no section for partial equations, I will put the question here. (x^2 -x -21)/(2x^3-x^2+8x-4) Thank you, Alexus      Log On


   

Question 32057: Since there is no section for partial equations, I will put the question here.
(x^2 -x -21)/(2x^3-x^2+8x-4)
Thank you,
Alexus
Answer by mukhopadhyay(490) About Me  (Show Source):
You can put this solution on YOUR website!
(x^2 -x -21)/(2x^3-x^2+8x-4)
=(x^2 -x -21)/(2x-1)(x^2+4)
Let (x^2 -x -21)/(2x-1)(x^2+4) = A/(2x-1)+(Bx+C)/(x^2+4)
So,
x^2 -x -21 = A((x^2+4)+(Bx+C)(2x-1)..............(1)
For x=1/2:
1/4-1/2-21=A(1/4+4)
=>(21-42-4)/84 = A(17/4)
=>-25/21=17A
=> A=-25/(21*17) = -25/357;
For x=0
-21=4A-C
=>C=4A+21; substitute the value of A to get C
For x=1
-21=5A+B+C
substitute the value of A and C to get B
After you get A, B, and C, use equation (1) to express the given equation in Partial Factor Decomposition form