Question

19. simplificati fractia ordinara f=1+2+3...+74/75+76+77...+999 pana devine ireductabila
DAU COROANA VA ROG!!!!!​

Answer 1

$f = \dfrac{1+2+3...+74}{75+76+77...+999} =$

$= \dfrac{\dfrac{74 \cdot 75}{2}}{\dfrac{999 \cdot 1000}{2} - \dfrac{74 \cdot 75}{2}}$

$= \dfrac{74 \cdot 75}{999 \cdot 1000 - 74 \cdot 75}$

$= \dfrac{74 \cdot 75}{74 \cdot 75(180 -1)} = \dfrac{1}{179}$