1. The problem is to solve the equation shown in the image: $$\frac{2x+3}{x-1} = 4$$. 2. The formula used here is to solve rational equations by eliminating the denominator: multiply both sides by the denominator to clear the fraction. 3. Multiply both sides by $x-1$: $$\cancel{\frac{2x+3}{x-1}} \times (x-1) = 4 \times (x-1)$$ which simplifies to: $$2x + 3 = 4(x - 1)$$ 4. Expand the right side: $$2x + 3 = 4x - 4$$ 5. Rearrange terms to isolate $x$: $$2x + 3 - 4x = -4$$ $$-2x + 3 = -4$$ 6. Subtract 3 from both sides: $$-2x + \cancel{3} - \cancel{3} = -4 - 3$$ $$-2x = -7$$ 7. Divide both sides by $-2$: $$\frac{-2x}{\cancel{-2}} = \frac{-7}{-2}$$ $$x = \frac{7}{2}$$ 8. The solution is $x = \frac{7}{2}$ or $3.5$. 9. Check that $x \neq 1$ to avoid division by zero, which is true here. Final answer: $$x = \frac{7}{2}$$.