Question

Evaluate :4-√5/4+√5 + 4+√5/4-√5

Answer 1

The above solution is the right solution

Our questions can be written in the format
4+√5/4-√5 + 4-√5/4+√5

or 4-√5/4+√5 + 4+√5/4-√5

Then the solution is
(4 +√5)/(4 -√5) + (4 -√5)/(4 +√5)
now dividing and multiplying the first term by (4 +√5) and second term by (4 -√5), we get,
(4 +√5)×(4 +√5)/(4 -√5)×(4 +√5) + (4 -√5)×(4 -√5)/(4 +√5)×(4 -√5)
⇒(4 +√5)²/(16 -5) + (4 -√5)²/(16 -5) ( applying (a² -b²) = (a+b)(a -b))
⇒(16 +5 +8√5 +16 +5 - 8√5)/11
⇒42/11