9. Si \( A \) es los \( 2 / 3 \) de \( 9 / 7 \) y \( B \) es los \( 5 / 4 \) de los \( 2 / 3 \). Hallar \( A-B \). \( \begin{array}{lll}\text { a) } 1 / 21 & \text { b) } 1 / 42 & \text { c) } 6 / 7 \\ \text { d) } 5 / 6 & \text { e) N.A. } & \end{array} \)
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Primero, calculemos \( A \): \[ A = \frac{2}{3} \times \frac{9}{7} = \frac{18}{21} = \frac{6}{7}. \] Ahora, calculemos \( B \): \[ B = \frac{5}{4} \times \frac{2}{3} = \frac{10}{12} = \frac{5}{6}. \] Finalmente, hallamos \( A - B \): \[ A - B = \frac{6}{7} - \frac{5}{6}. \] Para restar estas fracciones, encontramos un denominador común, que es \( 42 \): \[ A = \frac{6}{7} = \frac{36}{42} \quad \text{y} \quad B = \frac{5}{6} = \frac{35}{42}. \] Entonces, \[ A - B = \frac{36}{42} - \frac{35}{42} = \frac{1}{42}. \] La respuesta es \( \frac{1}{42} \), así que la opción correcta es \( \text{b) } 1 / 42 \).