Question

Can u answer this question?

Answer 1

if the question is an objective question

Answer 2

Answer: √5-√3

Explanation:

`\displaystyle\\(1)/(√(5)+√(3) ) +(1)/(2) (√(5) -√(3))\\`

Let us reduce this expression to a common denominator:

`\displaystyle\\(1+(1)/(2)(√(5)-√(3))(√(5)+√(3)) )/(√(5) +√(3) ) =\\\\(1+(1)/(2)((\sqrt5)^2 -(√(3) )^2) )/(√(5)+√(3) ) =\\\\(1+(1)/(2)(5-3) )/(√(5) +√(3) ) =\\\\(1+(1*2)/(2) )/(√(5) +√(3)) =\\\\(1+1)/(√(5) +√(3) ) =\\\\(2)/(√(5)+√(3) )`

Let's get rid of the irrationality in the denominator:

`\displaystyle\\(2(√(5)-√(3) ) )/((√(5) +√(3))(√(5) -√(3)) ) =\\\\(2(√(5)- √(3) ))/((√(5))^2-(√(3))^2 )=\\\\(2(√(5) -√(3)) )/(5-3) =\\\\(2(√(5)-√(3)) )/(2) =\\\\√(5)-√(3)`