Question

Simplificati fractia 5 la puterea n+1 +2x5 la puterea n + 5 la puterea n+2 supra 3 la puterea n+2 +2x3 la puterea n+1 + 3 la puterea n pana obtineti fractie ireductibila

Answer 1

$\frac{5 ^{n+1} + 2*5^{n} + 5^{n+2} }{ 3^{n+2} + 2*3^{n+1} + 3^{n} }$ = 

$\frac{ 5^{n}(5+2+ 5^{2})  }{ 3^{n}( 3^{2} +2+1)}$ = 

$\frac{ 5^{n}(5+2+ 25)  }{ 3^{n}( 9 +2+1)}$ = 

$\frac{ 5^{n} * 32)  }{ 3^{n}* 12}$ =  $\frac{ 5^{n} * 8)  }{ 3^{n}* 3}$ =  $\frac{ 5^{n} * 5+3)  }{ 3^{n}* 3}$ =  $\frac{ 5^{n+1} +3)  }{ 3^{n+1}}$