Question

If $\frac{3x+2}{(x+1)(2x^2+3)} = \frac{A}{x+1}+ \frac{Bx+C}{2x^2+3}$, then A - B + C=

• A. 2
• B. 1
• C. 3
• D. 6

Answer 1

Answer: (A)

2

Answer 2

The correct option is (A) 2.

comparing the left-hand side (LHS) and right-hand side (RHS) of the given expression, we arrive at the equation 3 x +2=A(2 x 2+3)+(Bx +C)(x +1). To determine the values of A , B , and C , we examine the coefficients of 2 x 2, x , and the constant term. By comparing these coefficients, we obtain the equations 0=2 A +B , 3=B +C , and 2=3 A +C. Subtracting the first equation from the third equation yields A − B +C =2.