Factor out the common term \(2\).
\[\frac{2}{x+1}-\frac{1}{2x+3}=\frac{3}{2(x+1)}\]
Multiply both sides by the Least Common Denominator: \(2(x+1)(2x+3)\).
\[4(2x+3)-2(x+1)=3(2x+3)\]
Simplify.
\[6x+10=6x+9\]
Cancel \(6x\) on both sides.
\[10=9\]
Since \(10=9\) is false, there is no solution.
[No Solution]
