SOLUTION: I want to find the value of a, b, and c so that i can decompose it into partial functions (8x-3)/(2x^2-x) thanks!!!

Algebra ->  Rational-functions -> SOLUTION: I want to find the value of a, b, and c so that i can decompose it into partial functions (8x-3)/(2x^2-x) thanks!!!       Log On


   

Question 277164: I want to find the value of a, b, and c so that i can decompose it into partial functions
(8x-3)/(2x^2-x)
thanks!!!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
%288x-3%29%2F%282x%5E2-x%29 = %288x-3%29%2Fx%282x-1%29
Write the given expression as a sum using A & B
%288x-3%29%2Fx%282x-1%29 = A%2Fx + B%2F%282x-1%29
:
Simplify by multipling each side by the LCD, x(2x-1)
x(2x-1)*%288x-3%29%2Fx%282x-1%29 = x(2x-1)*A%2Fx + x(2x-1)*(B%2F%282x-1%29
Results
8x - 3 = A(2x-1) + Bx
:
8x - 3 = A2x - A + Bx
:
8x - 3 = x(2A + B) - A
The coefficient on one side = the coefficient on the other side
2A + B = 8
the constant on one side = the constant on the other side
-A = -3
A = 3
Substitute 3 for A and find B
2(3) + B = 8
B = 8 - 6
B = 2
So we have
%288x-3%29%2Fx%282x-1%29 = 3%2Fx + 2%2F%282x-1%29