Answer
$3=x$
Work Step by Step
I multiply the equation with $(x-1)(2x+3)$ to cancel the denominators, then the equation becomes: $-4(x-1)+2x+3=1\\-4x+4+2x+3=1\\-2x+7=1\\-2x+7-1=1-1\\-2x+6=0\\-2x+6+2x=0+2x\\6=2x\\6/2=2x/2\\3=x$
The numerators of the original equation are defined for this value, thus it is a valid solution.
