b) \( \frac{4}{\sqrt{5}-\sqrt{2}} \)

To rationalize the denominator of \( \frac{4}{\sqrt{5}-\sqrt{2}} \), we can multiply both the numerator and the denominator by the conjugate of the denominator, which is \( \sqrt{5}+\sqrt{2} \). This gives us: \[ \frac{4(\sqrt{5}+\sqrt{2})}{(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})} \] The denominator simplifies as follows: \[ (\sqrt{5})^2 - (\sqrt{2})^2 = 5 - 2 = 3 \] Now we substitute back into the expression: \[ \frac{4(\sqrt{5}+\sqrt{2})}{3} \] So the rationalized form of \( \frac{4}{\sqrt{5}-\sqrt{2}} \) is: \[ \frac{4\sqrt{5}+4\sqrt{2}}{3} \] And there you have it—a rationalized expression that’s easy to work with!