#### Answer

$a=\dfrac{1}{2}$

#### Work Step by Step

$\dfrac{4}{a-1}+2=\dfrac{3}{a-1}$
Multiply the whole equation by $a-1$:
$(a-1)\Big(\dfrac{4}{a-1}+2=\dfrac{3}{a-1}\Big)$
$4+2(a-1)=3$
Solve for $a$:
$4+2a-2=3$
$2a+2=3$
$2a=3-2$
$2a=1$
$a=\dfrac{1}{2}$
Since the initial equation is not undefined for this value of $a$, we have found the answer. The solution to this equation is $a=\dfrac{1}{2}$