Rationalizing the denominator and simplifying the expression, the result is 6√5 + 13.
Option C is the correct answer.
What is the simplified form of this expression?
Given that;
[tex]\frac{4+\sqrt{5} }{\sqrt{5} -2}[/tex]
To rationalize the denominator, we multiply the expression by [tex]\frac{\sqrt{5} +2 }{\sqrt{5} +2}[/tex]
Hence
[tex]\frac{4+\sqrt{5} }{\sqrt{5}-2 } *\frac{\sqrt{5} +2 }{\sqrt{5} +2}\\\\\\\frac{(4+\sqrt{5}) }{(\sqrt{5}-2) } \frac{(\sqrt{5} +2) }{(\sqrt{5} +2)}\\\\\\\frac{(4+\sqrt{5})(\sqrt{5}+2) }{\sqrt{5}^2+\sqrt{5}*2-2\sqrt{5} -4 } \\\\\\\frac{(4+\sqrt{5} )(\sqrt{5}+2 )}{1}\\ \\(4+\sqrt{5} )(\sqrt{5}+2 )\\\\4\sqrt{5}+4*2+\sqrt{5}\sqrt{5}+\sqrt{5}*2\\ \\ 4\sqrt{5}+8+5+2\sqrt{5}\\ \\ 6\sqrt{5}+13[/tex]
Rationalizing the denominator and simplifying the expression, the result is 6√5 + 13.
Option C is the correct answer.
Learn more about how to Rationalize denominator here:https://brainly.com/question/27485639
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