Answer:
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Step-by-step explanation:
Answer:
12x=4y........................................
The partial fraction decomposition is 
<h3>How to determine the decomposition?</h3>
The fraction is given as:

Split the fraction as follows:

Take the LCM

Cancel the common factors
8x + 19 = Ax - A + Bx + 8B
By comparison, we have:
Ax + Bx = 8x
-A + 8B = 19
This gives
A + B = 8
-A + 8B = 19
Add both equations
9B = 27
Divide by 9
B = 3
Substitute B = 3 in A + B = 8
A + 3 = 8
Solve for A
A = 5
So, we have:

Hence, the partial fraction decomposition is 
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2r + 2s = 50
2r - s = 17
-----------subtract
3s = 33
s = 11
2r - s = 17
2r - 11 = 17
2r = 28
r = 14
so r = 14 and s = 11
answer is C. r = 14, s = 11