SOLUTION: find the value of a, b, and c so that i can decompose it to partial functions (3x -13)/(6x^2-x-12) thank you!

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Question 277166: find the value of a, b, and c so that i can decompose it to partial functions
(3x -13)/(6x^2-x-12)
thank you!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
find the value of a, b, and c so that i can decompose it to partial functions
%283x+-13%29%2F%286x%5E2-x-12%29 = %283x+-+13%29%2F%28%282x-3%29%283x%2B4%29%29
:
Write the given expression as a sum using A & B
%283x+-+13%29%2F%28%282x-3%29%283x%2B4%29%29 = A%2F%282x-3%29 + B%2F%283x%2B4%29
:
Multiply by the LCD, (2x-3)(3x+4)
(2x-3)(3x+4)%283x+-+13%29%2F%28%282x-3%29%283x%2B4%29%29 = (2x-3)(3x+4)A%2F%282x-3%29 + (2x-3)(3x+4)B%2F%283x%2B4%29
results
3x - 13 = A(3x+4) + B(2x-3)
:
3x - 13 = 3xA + 4A + 2xB - 3B
:
3x - 13 - (3A + 2B)x + 4A - 3B
Coefficients of x are equal
3A + 2B = 3
Constants are equal
4A - 3B = -13
;
Solve for two unknowns using elimination, multiply 1st eq by 3, 2nd eq by 2
9A + 6B = 9
8A - 6B =-26
----------------adding eliminates B, find A
17A = -17
A = -1
:
Find B
3A + 2B = 3
3(-1) + 2B = 3
-3 + 2B = 3
2B = 3 + 3
2B = 6
B = 3
:
We have
%283x+-+13%29%2F%286x%5E2-x-12%29 = -1%2F%282x-3%29 + 3%2F%283x%2B4%29
:
You should check this by adding the two fractions on the right to see if they equal the expression on the left