5²⁵-5²¹ / 5²²+5²⁴ = 24/5
Răspuns:
[tex]\bf\red\: \frac{5 {}^{25 } - 5 {}^{21} }{5 {}^{22} + 5 {}^{24} } \\ \\ \bf\red\:= \frac{5 {}^{4 + 21} - 5 {}^{21} }{5 {}^{22} + 5 {}^{2 + 22} } = \\ \\ \bf\red\:= \frac{5 {}^{4} \times 5 {}^{21 } - 5 {}^{21} }{5 {}^{22} + 5 {}^{2} \times 5 {}^{22} } = \\ \\\bf\red\: = \frac{(5 {}^{4} - 1) \times 5 {}^{21} }{(1 + 5 {}^{2}) \times 5 {}^{22} } = \\ \\\bf\red\: = \frac{(625 - 1) \times 5 {}^{21} }{(1 + 25) \times 5 {}^{22} } = \\ \\ = \bf\red\: \frac{625 - 1}{(1 + 25) \times 5} = \\ \\ \bf\red\: = \frac{624}{26 \times 5} \\ \\ = \bf\red\:\frac{24}{5} [/tex]
