Răspuns:
Explicație pas cu pas:
a) [tex]\frac{12}{\sqrt{3}} + \frac{15}{5\sqrt{3}} - 217\sqrt{3} + \frac{18}{\sqrt{3} }[/tex]
Rationalizam fractiile
[tex]\frac{12\sqrt{3} }{\sqrt{3}*\sqrt{3}} + \frac{15\sqrt{3} }{5\sqrt{3}*\sqrt{3}} - 217\sqrt{3} + \frac{18\sqrt{3} }{\sqrt{3}*\sqrt{3}}[/tex]
[tex]\frac{12\sqrt{3} }{3} + \frac{15\sqrt{3} }{5*3} - 217\sqrt{3} + \frac{18\sqrt{3} }{3} =[/tex]
[tex]\frac{12\sqrt{3} }{3} + \frac{15\sqrt{3} }{15} - 217\sqrt{3} + \frac{18\sqrt{3} }{3} =[/tex]
Aducem la acelasi numitor comun (15)
[tex]\frac{12*5\sqrt{3} }{3*5} + \frac{15\sqrt{3} }{15} - \frac{217*15\sqrt{3}}{15} + \frac{18*5\sqrt{3} }{3*5}[/tex]
[tex]\frac{60\sqrt{3} }{15} + \frac{15\sqrt{3} }{15} - \frac{3255\sqrt{3}}{15} + \frac{90\sqrt{3} }{15} =[/tex]
[tex]\frac{60\sqrt{3} + 15\sqrt{3} - 3255\sqrt{3} + 90\sqrt{3}}{15}=[/tex]
[tex]\frac{165\sqrt{3} - 3255\sqrt{3}}{15}[/tex]
[tex]\frac{-3090\sqrt{3}}{15}[/tex]
Simplificam prin 15
[tex]\frac{-206\sqrt{3}}{1} = -206\sqrt{3}[/tex]
b) [tex]\frac{8}{3\sqrt{2}} - \frac{8}{2\sqrt{2}} + \frac{8}{6\sqrt{2}} - \frac{8}{12\sqrt{2} }[/tex]
Rationalizam fractiile
[tex]\frac{8\sqrt{2} }{3\sqrt{2}*\sqrt{2}} - \frac{8\sqrt{2} }{2\sqrt{2}*\sqrt{2}} + \frac{8\sqrt{2} }{6\sqrt{2}*\sqrt{2}} - \frac{8\sqrt{2} }{12\sqrt{2} *\sqrt{2}}[/tex]
[tex]\frac{8\sqrt{2} }{3*2} - \frac{8\sqrt{2} }{2*2} + \frac{8\sqrt{2} }{6*2} - \frac{8\sqrt{2} }{12*2}[/tex]
[tex]\frac{8\sqrt{2} }{6} - \frac{8\sqrt{2} }{4} + \frac{8\sqrt{2} }{12} - \frac{8\sqrt{2} }{24}[/tex]
Aducem la acelasi numitor comun (24)
[tex]\frac{8*4\sqrt{2} }{6*4} - \frac{8*6\sqrt{2} }{4*6} + \frac{8*2\sqrt{2} }{12*2} - \frac{8\sqrt{2} }{24}[/tex]
[tex]\frac{32\sqrt{2} }{24} - \frac{48\sqrt{2} }{24} + \frac{16\sqrt{2} }{24} - \frac{8\sqrt{2} }{24}[/tex]
[tex]\frac{32\sqrt{2}- 48\sqrt{2} + 16\sqrt{2} - 8\sqrt{2}}{24}[/tex]
[tex]\frac{- 8\sqrt{2}}{24}[/tex]
Simplificam prin 8
[tex]\frac{- 1\sqrt{2}}{4}[/tex]
Urmatoarele doua se rezolva similar cu primele.
