You have $\displaystyle x= \frac{y- 1}{2y+ 3}$.
Multiply both sides by2y+3: $\displaystyle x(2y+ 3)= 2yx+ 3x= y- 1$.
Subtract 3x and y from both sides: $\displaystyle 2yx- y= -3x- 1$
Factor y out on the left: $\displaystyle y(2x- 1)= -3x- 1$
Divide both sides by 2x- 1: $\displaystyle y= -\frac{3x+ 1}{2x- 1}$.