Question

Punctul b de jos dar va rog si cu explicatii ofer coroana

Answer 1

Putem scrie: 
$2^{n+2}=2^2*2^n$
$2^{n+1}=2*2^n$
$3^{n+2}=3^2*3^n$

Inlocuim astea in exercitiu:
$\frac{36*6^n-2^{n+2}*3^{n+1}-2^{n+1}*3^{n+2}}{36*6^n-6*6^n-21*6^n}=$$\frac{36*6^n-2^2*2^n*3*3^n-2*2^n*3^2*3^n}{36*6^n-6*6^n-21*6^n}=$$\frac{36*6^n-12*2^n*3^n-18*2^n*3^n}{36*6^n-6*6^n-21*6^n}=$

(am inmultit numere cu numere, avem voie pt ca inmultirea e comutativa).
$2^n*3^n=6^n.$
Dam factor comun pe $6^n$ si la numarator si la numitor si obtinem:
$\frac{6^n(36-12-18)}{6^n(36-6-21)}= \frac{6^n*6}{6^n*9}=\frac{2}{3}$

(am simplificat $6^n$ si 6 si 9 prin 3.