\textbf{124--} The locus of the intersection of the asymptotes of the hyperbola $y=\dfrac{ax+3}{(a+1)x+(a-1)}$ is $y=\dfrac{3}{2}x^{2}+x+\dfrac{5}{6}$. The graph of this hyperbola intersects the $x$-axis at which length?
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(1) $3$ \hfill (2) $-3$ \hfill (3) $\dfrac{3}{2}$ \hfill (4) $-\dfrac{3}{2}$
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