Notăm raportul astfel:
[tex]\dfrac{a}{b} = \dfrac{2}{3} \implies \dfrac{a}{2} = \dfrac{b}{3} = k[/tex]
de unde a = 2k și b = 3k. Acum înlocuim și simplificăm la final
[tex]\dfrac{a}{a+b} = \dfrac{2k}{2k+3k} = \dfrac{2k}{5k} = \bf\dfrac{2}{5}\\[/tex]
[tex]\dfrac{2a+b}{a+2b} = \dfrac{4k+3k}{2k+6k} = \dfrac{7k}{8k} = \bf\dfrac{7}{8}\\[/tex]
[tex]\dfrac{2a-b}{2b-a} = \dfrac{4k-3k}{6k-2k} = \dfrac{k}{4k} = \bf\dfrac{1}{4}\\[/tex]
[tex]\dfrac{3a+2b}{2b-a} = \dfrac{6k+6k}{6k-2k} = \dfrac{12k}{4k} = \bf 3\\[/tex]
[tex]\dfrac{b-a}{2a-b} = \dfrac{3k-2k}{4k-3k} = \dfrac{k}{k} = \bf 1\\[/tex]
