3 + 5 ______ _____ = √3+√2 + √3-√2

Question

3 + 5
______ _____ =
√3+√2 + √3-√2

Answer 1

3 / (√3+√2) + 5 / (√3-√2) =
= 3*(√3-√2) / ( (√3+√2)(√3-√2) ) + 5*(√3+√2) / ( (√3+√2)(√3-√2) ) =
= ( 3*(√3-√2) +  5*(√3+√2)) / ( (√3+√2)(√3-√2) )  =
= ( 3√3 -3√2 +  5√3+5√2 ) / ( (√3) ^2-(√2)^2 ) =
= (8√3 + 2√2) / (3 - 2) = 8√3 + 2√2