Question

Quanto é X - 1/X - 1/ X - 1? Para x=5/2


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Answer 1

Explicação passo-a-passo:

$x-\frac{1}{x-\frac{1}{x-1}}$          e       $x=\frac{5}{2}$

substitua o valor de x na expressão

$\frac{5}{2}-\frac{1}{\frac{5}{2}-\frac{1}{\frac{5}{2}-1}}$

$\frac{5}{2}-\frac{1}{\frac{5}{2}-\frac{1}{\frac{5-2}{2}}}$

$\frac{5}{2}-\frac{1}{\frac{5}{2}-\frac{1}{\frac{3}{2}}}$

$\frac{5}{2}-\frac{1}{\frac{5}{2}-1.\frac{2}{3}}$

$\frac{5}{2}-\frac{1}{\frac{5}{2}-\frac{2}{3}}$

$\frac{5}{2}-\frac{1}{\frac{15-4}{6}}$

$\frac{5}{2}-\frac{1}{\frac{11}{6}}$

$\frac{5}{2}-1.\frac{6}{11}$

$\frac{5}{2}-\frac{6}{11}=\frac{55-12}{22}=\frac{43}{22}$