prove that


$\frac{3 x+2}{2 x-3}=-\frac{3}{4}$


Given, $\frac{3 x+2}{2 x-3}=-\frac{3}{4}$

$\Rightarrow \quad 4(3 x+2)=-3(2 x-3)$ [by cross-multiplication]

$\Rightarrow \quad 12 x+8=-6 x+9$

$\Rightarrow$ $12 x+6 x=9-8$ [transposing - $6 x$ to LHS and 8 to RHS]

$\Rightarrow$ $18 x=1$

$\Rightarrow$ $\frac{18 x}{18}=\frac{1}{18}$ [dividing both sides by 18]

$\therefore$ $x=\frac{1}{18}$

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