# SOLUTION: find the partial decomposition for the rational expression.

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 Algebra: Trigonometry Solvers Lessons Answers archive Quiz In Depth

 Question 88351: find the partial decomposition for the rational expression. 3/2x(3x+1) 3/2x(3x+1)=?/2x+?/3x+1 the question mark represent a blank spaceAnswer by stanbon(57387)   (Show Source): You can put this solution on YOUR website!find the partial decomposition for the rational expression. 3/2x(3x+1) 3/2x(3x+1)=?/2x+?/3x+1 the question mark represent a blank space ------------ 3/2x(3x+1) = A/2x + B/(3x+1) = [A(3x+1)+B(2x)]/[2x(3x+1)] Since the denominators are equal the numerators must be equal: [3Ax+A + 2Bx] = 3 (3A+2B)x + A = 0x + 3 A = 3 Therefore: 3A+2B = 0 3*3 + 2B = 0 2B = - 9 B = -4.5 =================== Final Answer: 3/2x(3x+1) = 3/2x - 4.5/(3x+1) ================ Cheers, Stan H.