Răspuns:
[tex]\frac{5}{12} =\frac{5}{12}[/tex], cele doua fractii sunt echivalente.
Explicație pas cu pas:
[tex](\frac{2}{3} )^5*(\frac{3}{2} )^3-(\frac{1}{2} -\frac{1}{3} )^2=\frac{10}{24}[/tex] amplificam fractia 1/2 cu 3 iar fractia 1/3 cu 2
[tex]\frac{2^5}{3^5} *\frac{3^3}{2^3} -(\frac{3}{6} -\frac{2}{6} )^2=\frac{10}{24}\\\\\frac{2^5*3^3}{3^5*2^3} -(\frac{1}{6} )^2=\frac{10}{24}\\\\\frac{3^3*2^2}{3^5} -\frac{1}{36} =\frac{10}{24}\\\\\frac{2^2}{3^2} -\frac{1}{36} =\frac{10}{24}\\\\\frac{4}{9} -\frac{1}{36} =\frac{10}{24}[/tex]amplificam fractia 4/9 cu 4
[tex]\frac{16}{36} -\frac{1}{36} =\frac{10}{24}\\\\\frac{15}{36} =\frac{10}{24}[/tex]simplificam fractia 15/36 cu 3 iar fractia 10/24 cu 2
[tex]\frac{5}{12} =\frac{5}{12}[/tex], cele doua fractii sunt echivalente.
Succes! :)
