Răspuns:
Explicație pas cu pas:
a / b = 0,(6) = 6 / 9 = 2 / 3
a / b = 2 / 3 => a = 2 si b = 3
( 3 a + 15 b ) / ( 12 a - 2 b ) = 17 / 6
= ( 3 × 2 + 15 × 3 ) : ( 12 × 2 - 2 × 3 ) =
= ( 6 + 45 ) : ( 24 - 6 ) =
= 51 / 18 = → simplific cu 3
= 17 / 6 =
= 2,8(3)
_____________________
sau:
⇒ 3 a = 2 b ⇒ b = 3 a / 2
_______________________
( 3 a + 15 b ) / ( 12 a - 2 b ) = 17 / 6 = 2,8(3)
= 3 × ( a + 5 b ) / 2 × ( 6 a - b ) =
= 3 × ( a + 5 × 3 a / 2 ) / 2 × ( 6 a - 3 a / 2 ) =
= 3 × ( 2 a / 2+ 15 a / 2) : [ 2 × ( 12 a / 2 - 3 a / 2 ) ] =
= 3 × ( 17 a / 2 ) : ( 2 × 9 a / 2 ) =
= ( 51 a / 2 ) : 9 a =
= ( 51 a / 2 ) × 1 / 9 a =
= 17 / ( 2 x 3 ) =
= 17 / 6
