#### Answer

The solutions are $x=4$ and $x=-\dfrac{3}{2}$

#### Work Step by Step

$\dfrac{x+4}{2x}=\dfrac{x-1}{3}$
Take $2x$ to multiply the numerator of the right side and $3$ to multiply the numerator of the left side:
$(x+4)(3)=(x-1)(2x)$
Evaluate the indicated operations:
$3x+12=2x^{2}-2x$
Take all terms to the right side and simplify:
$0=2x^{2}-2x-3x-12$
$0=2x^{2}-5x-12$
Rearrange:
$2x^{2}-5x-12=0$
Solve by factoring:
$(2x+3)(x-4)=0$
Set both factors equal to $0$ and solve each individual equation for $x$:
$2x+3=0$
$2x=-3$
$x=-\dfrac{3}{2}$
$x-4=0$
$x=4$
The solutions are $x=4$ and $x=-\dfrac{3}{2}$