Question

simplify
$\frac{5}{ \sqrt{3} + \sqrt{5} } + \frac{5}{ \sqrt{3} + \sqrt{5} }$
With proper explanation please !!!!
⚔️⚔️⚔️⚔️⚔️​

Answer 1

$\huge{\mathfrak{Answer}}$

$\implies\frac{5}{ \sqrt{3} + \sqrt{5} } + \frac{ 5 }{ \sqrt{3} + \sqrt{5} } \\ \\ \implies \frac{10}{ \sqrt{3} + \sqrt{5} }$

Till here, we have just simply took the lcm √3+√5 and added it.

While moving to the next step, we will Rationalise the denominator.

$\implies\frac{10}{ \sqrt{3} + \sqrt{5} } \times \frac{ \sqrt{3} - \sqrt{5} }{ \sqrt{3} - \sqrt{5} } \\ \\ \implies \frac{10( \sqrt{3} - \sqrt{5}) }{( { \sqrt{3)} )}^{2} - ( { \sqrt{5}) }^{2} } \\ \\ \implies \frac{10( \sqrt{3} - \sqrt{5} )}{3 - 5} \\ \\ \implies \frac{10( \sqrt{3} - \sqrt{5} )}{ - 2} \\ \\ \implies - 5( \sqrt{3} - \sqrt{5})$

Additional Information

If the denominator of any fraction is a root, then me Multiply the denominator of it by taking it's conjugate,and make the denominator in simple form.

Conjugate, means the negative of that.

for understanding it,

Suppose, we have to Rationalise, $\frac{a}{ \sqrt{3} - \sqrt{2} }$

So, we would take the conjugate as $\sqrt{3}+{2}$

$\frac{a}{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} }$

In the numerator, we would Multiply it simply by a, and in the denominator we would solve it on the formula $(a-b)(a+b) = (a)^{2} - b^{2}$

Thus,

$\frac{ a \sqrt{3} + a \sqrt{2} }{ \sqrt{3}^2 - \sqrt{2}^2}$

We got $\frac{ a \sqrt{3} + a \sqrt{2} }{3-2}$

$\frac{ a \sqrt{3} + a \sqrt{2} }{1}$

$a \sqrt{3} + a \sqrt{2}$

Answer 2

Answer:

5/√3+√5+5/√3+√5

10/√3+√5

10√3-10√5/3-5

10√3-10√5/-2

5√5-5√3

Step-by-step explanation: