Jawabanmu

2014-08-30T21:36:49+07:00
Pertama, sederhanakanlah dahulu baru.
\frac{x}{a}[1-\frac{b^{2}}{x^{2}}]+\frac{x}{b}[1-\frac{a^{2}}{x^{2}}]
=> x(\frac{1}{a}+\frac{1}{b})-(\frac{b^{2}}{a}+\frac{a^{2}}{b})
Sekarang, substitusikan x = a+b, maka
=> (a+b)(\frac{1}{a}+\frac{1}{b})-(\frac{b^{3}}{ab}+\frac{a^{3}}{ab})
=> [\frac{(a+b)b}{ab}+\frac{(a+b)a}{ab}]-(\frac{b^{3}}{ab}+\frac{a^{3}}{ab}) = \frac{ab+b^{2}+a^{2}+ab-b^{3}-a^{3}}{ab}= \frac{2ab+a^{2}(1-a)+b^{2}(1-b)}{ab}
=>  \frac{ab[2+a(1-a)+b(1-b)]}{ab}=2+a(1-a)+b(1-b)

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