Question

simplify 5+√3/7-4√3 + 5+√3 / 7 + 4√3

Answer 1

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Answer 2

Answer:

$70+14\sqrt{3}$

Step-by-step explanation:

Here, the given expression is,

$\frac{5+\sqrt{3}}{7-4\srt{3}}+\frac{5+\sqrt{3}}{7+4\sqrt{3}}$

$=\frac{(5+\sqrt{3})(7+4\sqrt{3})+(5+\sqrt{3})(7-4\sqrt{3})}{7^2-(4\sqrt{3})^2}$

( By using identity (a+b)(a-b) = a² - b² in denominator )

$=\frac{35+7\sqrt{3}+20\sqrt{3}+12+35+7\sqrt{3}-20\sqrt{3}-12}{49-48}$

$=\frac{70+14\sqrt{3}}{1}$

$=70+14\sqrt{3}$