#### Answer

$x=-\dfrac{3(a-1)}{a^{2}-a-1}$

#### Work Step by Step

$\dfrac{x}{a-1}=ax+3$
Take $a-1$ to multiply the right side:
$x=(ax+3)(a-1)$
Evaluate the product indicated on the right side:
$x=a^{2}x-ax+3a-3$
Take all terms with $x$ to the left side:
$x-a^{2}x+ax=3a-3$
Take out common factor $x$ from the left side:
$x(1-a^{2}+a)=3a-3$
Take $1-a^{2}+a$ to divide the right side:
$x=\dfrac{3a-3}{1-a^{2}+a}$
Take out common factor $3$ from the numerator to show a better looking answer:
$x=-\dfrac{3(a-1)}{a^{2}-a-1}$