Question

simplify 3/5√3-2/5+√3​

Answer 1

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To rationalize the denominator we must multiply the fraction by the appropriate form of 1 to eliminate the radicals from the denominator.

For a denominator of the type (a - b) we need to multiply by (a + b):

$(5 + \sqrt(3))/(5 + \sqrt(3)) * 2/(5 - \sqrt(3)) =>$

$(2(5 + \sqrt(3)))/((5 + \sqrt(3)) * (5 - \sqrt(3))) =>$

$(2 * 5 + 2\sqrt(3))/((5 * 5) - 5\sqrt(3) + 5 \sqrt(3) - \sqrt(3)\sqrt(3)) =>$

$(10 + 2\sqrt(3))/(25 - 0 - 3) =>$

$(10 + 2\sqrt(3))/22 =>$

$(5 + \sqrt(3))/11 =>$

Or

$5/11 + \sqrt(3)/11$

Hence the Answer is=$\frac{5}{11}+\frac{\sqrt{3} }{11}$