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EAMCET Engineering 2004 Solved Paper

Section: Mathematics

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Question : 91 of 160

Marks: +1, -0

If

\; \frac{x+1}{(2x-1)(3x+1)} = \frac{A}{2x-1} + \frac{B}{3x+1}

16A + 9B

4
5
6
8

Solution:

Given that,

\;\; \frac{x+1}{(2x-1)(3x+1)} = \frac{A}{2x-1} + \frac{B}{3x+1}

\Rightarrow (x+1) = A(3x+1) + B(2x-1)

\Rightarrow (x+1) = x(3A+2B) + A - B

On equating the coefficient of

x

and constant on both sides, we get

3A+2B = 1

. . . (i)

and

A-B = 1

. . . (ii)

On solving Eqs. (i) and (ii), we get

A = \frac{3}{5}, \; B = -\frac{2}{5}

\therefore \;\; 16A+9B = 16 \left(\frac{3}{5}\right) + 9 \left(-\frac{2}{5}\right)

\; = \frac{48}{5} - \frac{18}{5} = \frac{30}{5} = 6

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