a/b + a/c = 1 intreg si 1/7
a/b + a/c = 8/7
b este de 3 ori mai mic decat c => b = c : 3 => c = 3b
a/b + a/3b = 8/7
Amplificam prima fractie cu 3.
3a/3b + a/3b = 8/7
(3a+a)/3b = 8/7
4a/3b = 8/7
4a × 7 = 3b × 8
28a = 24b
Impartim la 2.
14a = 12b
Impartim iarasi la 2.
7a = 6b => a × 7 = 6b => a = 6b : 7 => a = 6b/7
6b/7 + 6b/7/3b = 8/7
6b/7 + 6b/7 × 1/3b = 8/7
6b/7 + 6b/21b = 8/7
Inmultim tot randul cu 7.
6b + 6b/3 = 8
6b + 2b = 8
8b = 8
b = 1
c = 3b => c = 3 × b = 3 × 1 = 3
a = 6b/7 = 6 × 1/7 = 6/7
a/b = 6/7/1 = 6/7
a/c = 6/7/3 = 6/7 × 1/3 = 2/7
Deci fractiile sunt:
6/7 si 2/7
Proba:
6/7 + 2/7 = 8/7 = 1 intreg si 1/7 (adevarat)
