1/x+1/y(polynomials)

x = (a + b)^2 / a

So, 1/x = a/(a + b)^2

y = (a^2 - ab - 2b^2)/2b

So, 1/y = 2b/(a^2 - ab - 2b^2) = 2b/(a - 2b)(a + b)

1/x + 1/y

= a/(a + b)^2 + 2b/(a - 2b)(a + b)

= [1/(a + b)^2(a - 2b)][a(a - 2b) + 2b(a + b)]

= (a^2 + 2b^2)/(a + b)^2(a - 2b)