Rationalise the denominator of 3/5-root3+2/5+root 3

1.	Rationalise the denominator of 3/5-root3+2/5+root 3
Answer» Answer: $\boxed{\sf \dfrac{25 + \sqrt{3}}{22}}$ Step-by-step explanation: GIVEN that ; $\sf \frac{3}{5 - \sqrt{3} } + \frac{2}{5 + \sqrt{3} } \\ \\ \bf Taking \: LCM : \\ \\ \implies \sf \frac{3(5 + \sqrt{3} ) + 2(5 - \sqrt{3}) }{(5 - \sqrt{3} )(5 + \sqrt{3} )} \\ \\ \implies \sf \frac{15 + 3 \sqrt{3} + 10 - 2 \sqrt{3} }{(5) {}^{2} - ( \sqrt{3}) {}^{2} } \\ \\ \implies \sf \frac{25 + \sqrt{3} }{25 - 3} \\ \\ \implies \sf \frac{25 + \sqrt{3} }{22}$ HENCE, the answer is $\bf \dfrac{25 + \sqrt{3}}{22}$ _______________________ $\large{\underline{\underline{\mathfrak{\heartsuit \: Algebraic \: Identity : \: \heartsuit}}}}$ (a + b) (a - b) = a² - b² (a + b)² = a² + b² + 2AB (a - b)² = a² + b² - 2ab

Answer»

Answer:

$\boxed{\sf \dfrac{25 + \sqrt{3}}{22}}$

Step-by-step explanation:

$\sf \frac{3}{5 - \sqrt{3} } + \frac{2}{5 + \sqrt{3} } \\ \\ \bf Taking \: LCM : \\ \\ \implies \sf \frac{3(5 + \sqrt{3} ) + 2(5 - \sqrt{3}) }{(5 - \sqrt{3} )(5 + \sqrt{3} )} \\ \\ \implies \sf \frac{15 + 3 \sqrt{3} + 10 - 2 \sqrt{3} }{(5) {}^{2} - ( \sqrt{3}) {}^{2} } \\ \\ \implies \sf \frac{25 + \sqrt{3} }{25 - 3} \\ \\ \implies \sf \frac{25 + \sqrt{3} }{22}$