Help with a Math problem?

Question

if f(x) = 4(numerator) 1+x^2 (denominator)

then find a simplified expression for:
f(x) + f(1/x) + f(1/x) (numerator) f(x) (denominator for last term)

could you please show the steps :) thanks

Answer 1

so this is this expresion:
((4/1+x^2)+ 1/(4/1+x^2)+ (1/(4/1+x^2)/(4/1+x^2))
so for the top, symplify and get:
(4/1+x^2)+(1+x^2)/4+ (1+x^2)^2/(16)
now get a common denominator of 16 (1+x^2):
(64+ 4(1+x^2)^2+(1+x^2)^3)/ 16 (1+x^2)=
(64+4(1+2x^2+x^4)+ 1+3x^2+3x^4+X^6)/16 (1+x^2)=
(69+11x^2+7x^4+x^6)/16(1+x^2)

Answer 2

f(x) = 4/(1+ x^2)
f(1/x) = 4/(1 + 1/(1/x)^2) = 4/(1+x^2)
f(x) +f(1/x) +f(1/x) = 12/(1+x^2)

Your last statement was confusing.