Question

Sejam a e b números reais para os quais a igualdade a/1+a + b/1+b = 1 determine o valor do produto a.b

Answer 1

$\dfrac{a}{a+1}+\dfrac{b}{b+1}=1$

$\dfrac{a(b+1)+b(a+1)}{(a+1)(b+1)}=1$

$ab+a+ab+b=(a+1)(b+1)$

$2ab+a+b=ab+a+b+1$

$2ab-ab+a+b-a-b=1$

$ab=1$

Answer 2

$\frac{1}{1+a}+\frac{b}{1+b}=1\\ \\ \frac{a(1+b)+b(1+a)}{(1+a)(1+b)}=1\\ \\ a+ab+b+ab=1+b+a+ab\\ \\ \boxed{ab=1}$