Question

Determinati valorile intregi nenule ale lui x pentru care
a)2x-1 |4x+7
b)2x-3 |4x+9
c)2x-1 |7x+13
d)7-2x |5x+18

Answer 1

a)    2x-1 / 4x+7
dar  2x-1 / 2x-1 => 2x-1 / 4x-2 
===========================scad din prima pe a doua =>
=> 2x-1/4x+7 -4x+2 => 2x-1 /9 => 2x-1 e {1,3,9} =>2x e  {2,4,10} =>
 =>x e{1,2,5}

d)    7-2x / 5x +18 (inmultesti cu 2 ) => 7-2x / 10x+36
dar  7-2x/ 7-2x       (inmultesti cu 5)=>  7-2x / 35-10x
=====================================le adunam =>
=> 7-2x /10x+18 +35-10x => 7-2x/53 => 7-2x e{1,53} =>
=> -2x e{-6,46} => x e {3,-23}

rationamentul e la fel pt b ), c)