what is the partial fraction decomposition in terms of x?
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In the middle equation on the left side, if you let x = 3/2, then the term containing A vanishes and you can solve for B :
12*(3/2) - 25 = A (2*(3/2) - 3) + B
18 - 25 = A * (3 - 3) + B
B = -7
which makes the last option the correct answer.