1. **State the problem:** We are given the function $$f(x) = \frac{6x+5}{2-\sqrt{14+5x}}$$ and we want to analyze or simplify it. 2. **Identify the domain:** The expression under the square root must be non-negative: $$14 + 5x \geq 0 \implies x \geq -\frac{14}{5}$$ Also, the denominator cannot be zero: $$2 - \sqrt{14 + 5x} \neq 0 \implies \sqrt{14 + 5x} \neq 2 \implies 14 + 5x \neq 4 \implies 5x \neq -10 \implies x \neq -2$$ 3. **Simplify the function:** To simplify, multiply numerator and denominator by the conjugate of the denominator: $$\frac{6x+5}{2 - \sqrt{14 + 5x}} \times \frac{2 + \sqrt{14 + 5x}}{2 + \sqrt{14 + 5x}} = \frac{(6x+5)(2 + \sqrt{14 + 5x})}{(2)^2 - (\sqrt{14 + 5x})^2}$$ 4. **Calculate the denominator:** $$4 - (14 + 5x) = 4 - 14 - 5x = -10 - 5x$$ 5. **Rewrite the function:** $$f(x) = \frac{(6x+5)(2 + \sqrt{14 + 5x})}{-10 - 5x}$$ 6. **Factor the denominator:** $$-10 - 5x = -5(2 + x)$$ 7. **Final simplified form:** $$f(x) = \frac{(6x+5)(2 + \sqrt{14 + 5x})}{-5(2 + x)}$$ **Domain:** $$x \geq -\frac{14}{5}$$ and $$x \neq -2$$