jika a . b . c = 1 maka ekspresi. [tex] \frac{1}{1+a+ b^{-1} } [/tex] + [tex] \frac{1}{1+b+ c^{-1} } [/tex] + [tex] \frac{1}{1+c+ a^{-1} } [/tex] sama dengan..

jawab

a.b.c = 1
1/c = (ab)

[tex] \frac{1}{1 + a + \frac{1}{b} }\, + \frac{1}{1 + b + \frac{1}{c} }\, + \frac{1}{1+ c + \frac{1}{a} }\ = \\ \frac{b}{b + ab +1}\, + \frac{1}{1+ b + ab} \, + \frac{1}{1 + ab + \frac{1}{a} }\\ \frac{b}{b + ab +1}\, + \frac{1}{1+ b + ab} \, + \frac{ab}{ab +1 +b}\\ = \frac{b+1 + ab }{b + ab + 1} \\ = 1 [/tex]