Find the value of \( \frac{1}{(\sqrt{4}-\sqrt{3})} \)

To find the value of \( \frac{1}{\sqrt{4}-\sqrt{3}} \), we can simplify the expression by rationalizing the denominator. We do this by multiplying both the numerator and the denominator by the conjugate of the denominator, which is \( \sqrt{4} + \sqrt{3} \). Let's perform the calculation: \[ \frac{1}{\sqrt{4}-\sqrt{3}} \cdot \frac{\sqrt{4} + \sqrt{3}}{\sqrt{4} + \sqrt{3}} = \frac{\sqrt{4} + \sqrt{3}}{(\sqrt{4})^2 - (\sqrt{3})^2} \] Now, compute the denominator: \[ (\sqrt{4})^2 - (\sqrt{3})^2 = 4 - 3 = 1 \] So, the expression simplifies to: \[ \frac{\sqrt{4} + \sqrt{3}}{1} = \sqrt{4} + \sqrt{3} \] Substituting \( \sqrt{4} = 2 \): \[ 2 + \sqrt{3} \] Thus, the final value of \( \frac{1}{\sqrt{4}-\sqrt{3}} \) is: \[ 2 + \sqrt{3} \]