Given the expression:
[tex]\frac{5}{1+\sqrt[]{3}}[/tex]
We will simplify the given expression to:
[tex]\frac{a+b\sqrt[]{c}}{d}[/tex]
The simplification will be as follows:
[tex]\frac{5}{1+ \sqrt[]{3} }\times\frac{1-\sqrt[]{3}}{1-\sqrt[]{3}}=\frac{5\cdot(1-\sqrt[]{3})}{1^2-(\sqrt[]{3})^2}=\frac{5\cdot1-5\cdot\sqrt[]{3}}{1-3}=\frac{5-5\sqrt[]{3}}{-2}[/tex]
Compare the result with
[tex]\frac{a+b\sqrt[]{c}}{d}[/tex]
So, the answer will be:
[tex]\begin{gathered} a=5 \\ b=-5 \\ c=3 \\ d=-2 \end{gathered}[/tex]
