Question

DAU COROANA+30 PUNCTE!
Simplificati fractia: $2^{n}$· $3^{n+1}$+$2^{n+2}$·$3^{n}$
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$3^{n}$·$5^{n+1}$+$3^{n+2}$·$5^{n}$

Answer 1

(2ⁿ·3ⁿ⁺¹+2ⁿ⁺²·3ⁿ)/(3ⁿ·5ⁿ⁺¹+3ⁿ⁺²·5ⁿ)=
=2ⁿ·3ⁿ(3¹+2²)/3ⁿ·5ⁿ(5¹+3²)=
=2ⁿ·7/5ⁿ·14=
=2ⁿ/5ⁿ·2=
=2ⁿ⁻¹/5ⁿ