Question

O valor de x na expressão (anexo)

a) 12/19
b) -12/19
c)19/12
d)17/12
e) 12/17

Answer 1

primeiro resolvemos um lado:
$0,111...+\frac{\frac{3}{11}}{\frac{1}{4}+\frac{1}{4}}$
1/9+6/11 mmc=99
11/99+54/99
0,111...=1/9 então seria 65/99

o segundo lado:
$\frac{\frac{1}{2}}{\frac{6}{5}}+\frac{1}{3}$
5/12+1/3 mmc=12
5/12+4/12=9/12

por último soma os dois
mmc=396
65/99 vira 260/396
9/12 vira 297/396
x=260/396+297/396=557/396 ou aprox. 1,4
não consegui chegar ao resultado , desculpe :/

Answer 2

$x= \left \{ 0,111...+\frac{\frac{3}{11}}{4^{-1}+\frac{1}{4}}\right \} + \left \{\frac{\frac{1}{2}}{0,2+14^0}+\frac{1}{3} \right \}$

$x= \left \{ \frac{1}{9}+\frac{\frac{3}{11}}{\frac{1}{4}+\frac{1}{4}}\right \} + \left \{\frac{\frac{1}{2}}{\frac{1}{5}+1}+\frac{1}{3} \right \} \\ \\ x= \left \{ \frac{1}{9}+\frac{\frac{3}{11}}{\frac{1}{2}}\right \} + \left \{\frac{\frac{1}{2}}{\frac{6}{5}}+\frac{1}{3} \right \} \\ \\ x= \left \{ \frac{1}{9}+\frac{3}{11}.\frac{2}{1}\right \} + \left \{\frac{1}{2}.\frac{5}{6}+\frac{1}{3} \right \}$

$x= \left \{ \frac{1}{9}+\frac{6}{11}\right \} + \left \{\frac{5}{12}+\frac{1}{3} \right \} \\ \\ x=\frac{11+54}{99}+\frac{5+4}{12} \\ \\ x=\frac{65}{99}+\frac{9}{12}=\frac{557}{396}$