$If \frac{px + q}{{(2 x - 3)}^{2}} = \frac{1}{(2 x - 3)} + \frac{3}{{(2 x - 3)}^{2}} then slope of the line px + 3 y + q = 0 is$

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$\frac{- 3}{2}$

$\frac{2}{3}$

$\frac{- 2}{3}$

$\frac{3}{2}$

answer is A.

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Detailed Solution

$\begin{array}{rcl} \frac{px + q}{{(2 x - 3)}^{2}} & = & \frac{1}{2 x - 3} + \frac{3}{{(2 x - 3)}^{2}} \\ px + q & = & 2 x - 3 + 3 = 2 x \\ p & = & 2, q = 0 \end{array}$

slope of line $2 x + 3 y = 0 is m = \frac{- 2}{3}$

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