Question

a,b € Z ; 2a=3b se cunoaste. 2a+b/12a-5b=?

Answer 1

 am trasformat in proportie 
a / 3 = b / 2 = k 
a = 3k           b = 2k 
( 2a + b)  / ( 12a - 5b ) = ( 6k + 2k ) / ( 36k  - 10 k) = 8k / 26k = 8 /26 = 4 /13 

Answer 2

    
[tex]\displaystyle 2a=3b \\ \\ \frac{2a+b}{12a-5b}= \frac{2a+b}{6\times 2a-5b} = ~~~~~Inlocuim ~pe~ 2a ~cu ~3b.\\ \\ = \frac{3b+b}{6\times 3b-5b}= \frac{3b+b}{18b-5b}= \frac{4b}{13b} = \boxed{\frac{4}{13}}[/tex]