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Sagot :
Answer:
Simplifying the given expression gives;
[tex]27+12\sqrt[]{5}[/tex]Explanation:
Given the expression;
[tex]\frac{6+3\sqrt[]{5}}{\sqrt[]{5}-2}[/tex]Multiplying both the denominator and numerator by the conjugate of the denominator;
[tex]\begin{gathered} \frac{6+3\sqrt[]{5}}{\sqrt[]{5}-2}\times\frac{\sqrt[]{5}+2}{\sqrt[]{5}+2}=\frac{(6+3\sqrt[]{5})(\sqrt[]{5}+2)}{(\sqrt[]{5}-2)(\sqrt[]{5}+2)} \\ =\frac{6\sqrt[]{5}+6\sqrt[]{5}+12+3(5)}{5-4} \\ =\frac{12\sqrt[]{5}+12+15}{1} \\ =27+12\sqrt[]{5} \end{gathered}[/tex]Therefore, simplifying the given expression gives;
[tex]27+12\sqrt[]{5}[/tex]
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