1. The problem is to solve the equation given 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. Bring all terms to one side to isolate $x$: $$2x + 3 - 4x + 4 = 0$$ which simplifies to: $$-2x + 7 = 0$$ 6. Solve for $x$: $$-2x = -7$$ $$\cancel{-2x} = \cancel{-7}$$ $$x = \frac{7}{2}$$ 7. Check the solution does not make the denominator zero: Denominator is $x-1$, for $x=\frac{7}{2}$, $\frac{7}{2} - 1 = \frac{5}{2} \neq 0$, so solution is valid. Final answer: $$x = \frac{7}{2}$$