Question

simplify by rationalising the denominator:-3/4√5+√3+2/4√5+√3​

Answer 1

$\huge{\underline{\bf\red{Questi{\mathbb{O}}n} :}}$

Simplify by rationalising the denominator :-

$\boxed{ \frac{3}{4 \sqrt{5} + \sqrt{3} } + \frac{2}{4 \sqrt{5} + \sqrt{3} } }$

$\huge{\underline{\bf\blue{Soluti{\mathbb{O}}n}\ :}}$

$\begin{aligned} \\ & \ \ \ \ \red{ \frac{3}{4 \sqrt{5} + \sqrt{3} } + \frac{2}{4 \sqrt{5} + \sqrt{3} } } \\ \\ & = \frac{3 + 2}{4 \sqrt{5} + \sqrt{3} } \\ \\ & = \frac{5}{4 \sqrt{5} + \sqrt{3} } \\ \\ & = \frac{5}{4 \sqrt{5} + \sqrt{3} } \times \frac{4 \sqrt{5} - \sqrt{3} }{4 \sqrt{5} - \sqrt{3} } \\ \\ & = \frac{5(4 \sqrt{5} - \sqrt{3} )}{(4 \sqrt{5} + \sqrt{3} )(4 \sqrt{5} - \sqrt{3} )} \\ \\ & = \frac{5(4 \sqrt{5} ) - 5( \sqrt{3} )}{ {(4 \sqrt{5} )}^{2} - {( \sqrt{3} )}^{2} } \\ \\ & = \frac{20 \sqrt{5} - 5 \sqrt{3} }{80 - 9} \\ \\ & = \boxed{ \blue{ \bf \frac{20 \sqrt{5} - 5 \sqrt{3} }{71}} } & & \end{aligned}$

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