Simplifyi:(7+3√5\3+√5)+(7-3√5\3-√5

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Solution

Q. (7 + 3√5) / (3 + √5) + (7 - 3√5) / (3 - √5)

Taking LCM (3 + √5) (3 - √5) and adding we get,

{(7 + 3√5) (3 - √5) + (7 - 3√5) (3 + √5)} / (3 + √5) (3 - √5)

Solving this we get,

12 / 3^2– (√5)^2[(3 + √5) (3 - √5) = 3^2 – (√5)^2using identity (a +b) (a – b) = a^2– b^2]

=12 / 9 – 5

=12 / 4

= 3

(Answer)

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