If px+q(2x−3)2=1(2x−3)+3(2x−3)2 then slope of the line px+3y+q=0 is

px+q=(2x−3)+3 ⇒P=2,q=0 Line is 2x+3y=0 ⇒slope =−23

If px+q(2x−3)2=1(2x−3)+3(2x−3)2 then slope of the line px+3y+q=0 is

px+q=(2x−3)+3 ⇒P=2,q=0 Line is 2x+3y=0 ⇒slope =−23

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

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$\frac{- 2}{3}$

$\frac{3}{2}$

$\frac{- 3}{2}$

$\frac{2}{3}$

answer is A.

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Detailed Solution

$p x + q = (2 x - 3) + 3 \Rightarrow P = 2, q = 0$
Line is $2 x + 3 y = 0$
$\Rightarrow s l o p e = \frac{- 2}{3}$

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If px+q(2x−3)2=1(2x−3)+3(2x−3)2 then slope of the line px+3y+q=0 is

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