Question

Aratati ca numarul:
a) N = $\frac{3x+12}{7}$ : $\frac{x+4}{21}$ este natural ,oricare ar fi x∈N;
b) N =$\frac{30}{2x+7}$ : $\frac{5}{6x+21}$ este natural ,oricare ar fi x∈N;

Answer 1

a) $\dfrac{3x+12}{7}: \dfrac{x+4}{21}=\dfrac{3x+12}{7} \cdot \dfrac{21}{x+4}=\dfrac{3(x+4)}{7}\cdot \dfrac{21}{x+4}= \dfrac{3(x+4)}{1} \cdot \dfrac{3}{x+4}=3 \cdot 3= 9$
9€ N

b) $\dfrac{30}{2x+7} : \dfrac{5}{6x+21}=\dfrac{30}{2x+7} \cdot \dfrac{6x+21}{5}=\dfrac{1}{2x+7} \cdot \dfrac{3(2x+7)}{1}=3$
3€N