Question

Which choice is equivalent to the fraction below when x is an appropriate
value? Hint: Rationalize the denominator and simplify.
Sqrt12/sqrt3 -3
O A. -1 - sqrt3
O B. -1 + sqrt3
O C. - sqrt3
O D.-1 - sqrt2

Answer 1

The rationalized form of the expression will be $-1+\sqrt{2}}$

Rationalization of rational functions

Given the rational function

$\frac{\sqrt{12}}{\sqrt{3}-3}$

Multiplying by the conjugate of the denominator

$=\frac{\sqrt{12}}{\sqrt{3}-3}\times \frac{\sqrt{3}+3}{\sqrt{3}+3}\\=\frac{\sqrt{12}(\sqrt{3}+3)}{3-9}\\ =\frac{(\sqrt{36}+3\sqrt{12})}{3-9}\\=\frac{6+6\sqrt{2}}{-6}\\ =$

Simplifying further will give:

$-1+\sqrt{2}}$

Hence the rationalized form of the expression will be $-1+\sqrt{2}}$

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