Bonjour,
Exprimer le résultat sous forme d'une fraction simplifiée au maximum si besoin :
a.
[tex] \frac{2}{ \red{3}} + \frac{1}{ \blue{2}} = \frac{2 \blue{\times 2}}{ \red{3} \blue{\times 2}} + \frac{1 \red{\times 3}}{ \blue{2 } \red{\times 3}} = \frac{4}{6} + \frac{3}{6} = \green{\boxed{ \frac{7}{6} }}[/tex]
b.
[tex] \frac{5}{ \orange{4}} - \frac{5}{ \purple{6}} = \frac{5 \purple{ \times 6}}{ \orange{4} \times \purple{6}} - \frac{5 \orange{ \times 4}}{ \purple{6}\orange{ \times4 }} = \frac{30}{24} - \frac{20}{24} \\ = \frac{10}{24} = \frac{2 \times 5}{2 \times 12} = \blue{ \boxed{ \frac{5}{12} }}[/tex]
c.
[tex] \frac{3}{ \green{10}} + \frac{9}{ \blue{12}} = \frac{3 \blue{ \times 12}}{ \green{10} \blue{ \times 12}} + \frac{9 \green{ \times 10}}{ \blue{12} \green{ \times 10}} = \frac{36}{120} + \frac{90}{120} \\ = \frac{126}{120} = \frac{6 \times 21}{6 \times 20} = \purple{ \boxed{ \frac{21}{20} }}[/tex]
Bonne journée
