Question

$\frac{ {2}^{65} - {2}^{63} }{ {2}^{66} + {2}^{67} }$
Scrieți fracția de mai sus sub formă de fracție ordinară ireductibilă

Answer 1

$\frac{2^{65}-2^{63}}{2^{66}+2^{67}}=\frac{2^{63}(2^{2}-1)}{2^{66}(1+2)}=\frac{4-1}{2^{3}*3}=\frac{3}{3*8}=\frac{1}{8}$

Answer 2

$\frac{ {2}^{65} - {2}^{63} }{ {2}^{66} + {2}^{67} } = \frac{ {2}^{63}( \frac{ {2}^{65} }{ {2}^{63} } - \frac{ {2}^{63} }{ {2}^{63} }) }{ {2}^{66}( \frac{ {2}^{66} }{ {2}^{66} } + \frac{ {2}^{67} }{ {2}^{66} }) } = \frac{ {2}^{63}( {2}^{65 - 63} - 1) }{ {2}^{66}(1 + {2}^{67 - 66}) } = \frac{ {2}^{63}( {2}^{2} - 1) }{ {2}^{66}(1 + 2) } = \frac{ {2}^{66}(4 - 1) }{ {2}^{66} \times 3 } = \frac{ {2}^{63} \times 3 }{ {2}^{66} \times 3 } = \frac{1}{ {2}^{66 - 63} } = \frac{1}{ {2}^{3} } = \frac{1}{8}$