invalsi numeri razionali

Numeratore :

2^-1 = 1/2^1 = 1/2

3^-2 = 1/3^2 = 1/9

1/2+1/9 = (9+2)/18 = 11/18

Denominatore

2^-2  =1/2^2 = 1/4

3^-1 = 1/3^1 = 1/3

1/3+1/4 = (4+3)/12 = 7/12

11/18 * 12/7 = 11*2 / 7*3 = 22/21

$\frac{2^{-1} + 3^{-2}}{2^{-2} + 3^{-1}} =$

$= (\frac{1}{2}+\frac{1}{3^2}):(\frac{1}{2^2}+\frac{1}{3}) =$

$= (\frac{1}{2}+\frac{1}{9}):(\frac{1}{4}+\frac{1}{3}) =$

$= (\frac{9+2}{18}):(\frac{3+4}{12}) =$

$= \frac{11}{18}:\frac{7}{12} =$

$= \frac{11}{18}×\frac{12}{7} =$

$= \frac{11}{3}×\frac{2}{7} =$

$= \frac{22}{21}$.

La risposta corretta è la C.