1. The problem is to solve the equation $$\frac{2x-3}{x+1} = 3$$ for $x$. 2. We use the property that if $$\frac{A}{B} = C$$, then $$A = B \times C$$, provided $B \neq 0$. 3. Multiply both sides of the equation by $x+1$ to eliminate the denominator: $$2x - 3 = 3(x + 1)$$ 4. Expand the right side: $$2x - 3 = 3x + 3$$ 5. Rearrange terms to isolate $x$: $$2x - 3x = 3 + 3$$ 6. Simplify both sides: $$-x = 6$$ 7. Multiply both sides by $-1$ to solve for $x$: $$x = -6$$ 8. Check the solution by substituting $x = -6$ back into the original equation: $$\frac{2(-6) - 3}{-6 + 1} = \frac{-12 - 3}{-5} = \frac{-15}{-5} = 3$$ which is true. Therefore, the solution is $$x = -6$$.