1. **State the problem:** We need to find the value of the constant $k$ such that the equation $$\frac{kx^2 + 14x - 20}{3x - 2} = 5x + 8 - \frac{4}{3x - 2}$$ holds true for all $x \neq \frac{2}{3}$. 2. **Rewrite the equation:** Multiply both sides by $3x - 2$ to eliminate the denominators (valid since $x \neq \frac{2}{3}$): $$k x^2 + 14 x - 20 = (5x + 8)(3x - 2) - 4$$ 3. **Expand the right side:** $$(5x + 8)(3x - 2) - 4 = (5x)(3x) + (5x)(-2) + 8(3x) + 8(-2) - 4$$ $$= 15 x^2 - 10 x + 24 x - 16 - 4$$ $$= 15 x^2 + 14 x - 20$$ 4. **Set the expressions equal:** $$k x^2 + 14 x - 20 = 15 x^2 + 14 x - 20$$ 5. **Compare coefficients:** Since the equation holds for all $x$, the coefficients of corresponding powers must be equal: - Coefficient of $x^2$: $k = 15$ - Coefficient of $x$: $14 = 14$ (already equal) - Constant term: $-20 = -20$ (already equal) 6. **Answer:** The value of $k$ is **15**. **Final answer:** $\boxed{15}$