Explanation
Given the expression
[tex]\frac{4}{3-\sqrt[]{5}}[/tex]
We can find the simplified format below
[tex]\begin{gathered} \frac{4}{3-\sqrt[]{5}} \\ \mathrm{Multiply\: by\: the\: conjugate}\: \frac{3+\sqrt{5}}{3+\sqrt{5}} \\ =\frac{4\left(3+\sqrt{5}\right)}{\left(3-\sqrt{5}\right)\left(3+\sqrt{5}\right)} \\ =\frac{12+4\sqrt[]{5}}{9+3\sqrt[]{5}-3\sqrt[]{5}-\sqrt[]{25}} \\ =\frac{12+4\sqrt[]{5}}{9-5} \\ =\frac{12+4\sqrt[]{5}}{4} \\ =\frac{4(3+\sqrt[]{5})}{4} \\ =3+\sqrt[]{5} \end{gathered}[/tex]
Answer:
[tex]3+\sqrt[]{5}[/tex]
