....... Bila f(x) = [tex]\frac{x}{a} [ \frac{b^2}{x^2} ] + \frac{x}{b} [1- \frac{a^2}{x^2} ][/tex] , maka f(a+b)= ...

[tex]f(x)= \frac{x}{a} [ \frac{b^2}{x^2}]+\frac{x}{b} [1- \frac{a^2}{x^2}] \\ f(a+b)=\frac{a+b}{a} [ \frac{b^2}{(a+b)^2}]+\frac{a+b}{b} [1- \frac{a^2}{(a+b)^2}] \\ =\frac{a+b}{a} . \frac{b^2}{(a+b)^2}+\frac{a+b}{b}-\frac{a+b}{b}. \frac{a^2}{(a+b)^2} \\ = \frac{b^2}{a(a+b)} +\frac{a+b}{b}- \frac{a^2}{b(a+b)} \\ = \frac{b^3+a(a+b)(a+b)-a^3}{ab(a+b)} \\ = \frac{b^3+a(a^2+2ab+b^2)-a^3}{ab(a+b)} \\ =\frac{b^3+a^3+2a^2b+ab^2-a^3}{ab(a+b)} \\ =\frac{b^3+2a^2b+ab^2}{ab(a+b)} [/tex]