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Simplify the terms sqrt(20) and sqrt(12).

Mathematics

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  1. Simplify the terms 20\sqrt{20} and 12\sqrt{12}.

    20=4×5=25\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5} 12=4×3=23\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}

    The expression to evaluate becomes:

    x+25x−25+x+23x−23\frac{x+2\sqrt{5}}{x-2\sqrt{5}} + \frac{x+2\sqrt{3}}{x-2\sqrt{3}}

  2. Manipulate the given value of xx.

    We are given x=4145+3x = \frac{4\sqrt{14}}{\sqrt{5}+\sqrt{3}}.
    Multiply

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