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Maths-

General

Easy

Question

$Lt subscript x not stretchy rightwards arrow a end subscript fraction numerator square root of a plus 2 x end root minus square root of 3 x end root over denominator square root of 3 a plus x end root minus 2 square root of x end fraction equals$

$\frac{2}{\sqrt{3}}$
$\frac{1}{\sqrt{3}}$
$\frac{- 2}{3 \sqrt{3}}$
$\frac{2}{3 \sqrt{3}}$

hint Hint:

In this question, firstly, we will rationalize the equation and simplify and then put the value of x.

The correct answer is: $fraction numerator 2 over denominator 3 square root of 3 end fraction$

$space space space Lt subscript x not stretchy rightwards arrow a end subscript fraction numerator square root of a plus 2 x end root minus square root of 3 x end root over denominator square root of 3 a plus x end root minus 2 square root of x end fraction R a t o n a l i sin g space t h e space n u m e r a t o r comma equals Lt subscript x not stretchy rightwards arrow a end subscript fraction numerator square root of a plus 2 x end root minus square root of 3 x end root over denominator square root of 3 a plus x end root minus 2 square root of x end fraction cross times fraction numerator square root of a plus 2 x end root plus square root of 3 x end root over denominator square root of a plus 2 x end root plus square root of 3 x end root end fraction cross times fraction numerator square root of 3 a plus x end root plus 2 square root of x over denominator square root of 3 a plus x end root plus 2 square root of x end fraction equals Lt subscript x not stretchy rightwards arrow a end subscript fraction numerator left parenthesis a plus 2 x minus 3 x right parenthesis open parentheses square root of 3 a plus x end root plus 2 square root of x close parentheses over denominator left parenthesis 3 a plus x minus 4 x right parenthesis open parentheses square root of a plus 2 x end root plus square root of 3 x end root close parentheses end fraction equals Lt subscript x not stretchy rightwards arrow a end subscript fraction numerator square root of 3 a plus x end root plus 2 square root of x over denominator 3 open parentheses square root of a plus 2 x end root plus square root of 3 x end root close parentheses end fraction equals fraction numerator square root of 3 a plus a end root plus 2 square root of a over denominator 3 open parentheses square root of a plus 2 a end root plus square root of 3 a end root close parentheses end fraction equals 1 third cross times fraction numerator 4 square root of a over denominator 2 square root of 3 a end root end fraction equals fraction numerator 2 over denominator 3 square root of 3 end fraction$

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