Răspuns:
Explicație pas cu pas:
Vom folosi urmatoarele formule:
[tex]\displaystyle\boxed{\frac{a}{y} +\frac{b}{y} =\frac{a+b}{y}} \\\displaystyle\boxed{\frac{a}{y} -\frac{b}{y} =\frac{a-b}{y} }[/tex]
Trecem la efectuarea calculelor
a)
[tex]\displaystyle\frac{5x}{9} +\frac{2x}{9} =\frac{5x+2x}{9} =\frac{7x}{9}[/tex]
b)
[tex]\displaystyle\frac{x}{y} +\frac{5x}{y} -\frac{12x}{y} =\frac{x+5x-12x}{y} =\frac{-6x}{y}[/tex]
c)
[tex]\displaystyle\frac{4x+1}{3a} -\frac{4x-2y-3}{3a} +\frac{5x+y}{3a} =\frac{\not4x+1-\not4x+2y+3+5x+y}{3a} =\frac{5x+3y+4}{3a}[/tex]
d)
Daca observam nu putem sa aplicam formula de mai sus deoarece nu avem numitorul comun
Ca sa aflam numitorul comun incercam sa aflam cel mai mic multiplu comun
Ca sa aflam acest lucru trecem la descompunerea numerelor dupa care vom lua numerele comune si necomune la puterea cea mai mare
6=2x3
4=2²
2=2
3=1
c.m.m.m.c=2²x34x3=12
[tex]\displaystyle\frac{5x}{6} -\frac{3y}{4} +\frac{y}{2} -\frac{2x}{3} =\frac{2\times5x}{12} -\frac{3\times3y}{12} +\frac{6\times y}{12} -\frac{4\times 2x}{12} =\frac{10x-9y+12y-8x}{12} =\frac{2x-3y}{12}[/tex]
e)
14=7x2
2=2
7=7
------------
c.m.m.m.c=7x2=14
[tex]\displaystyle\frac{x+2}{14} -\frac{2x-1}{2} +\frac{x-2}{7} =\frac{x+2}{14} -\frac{7(2x-1)}{14} +\frac{2(x-2)}{14} =\frac{x+\not2-14x+7+2x-\not2}{14} =\frac{7-11x}{14}[/tex]
f) observam ca factorul comun este 6a^2x^2
[tex]\displaystyle\frac{3a}{6ax^{2} } -\frac{x}{6a^{2}x } +\frac{a}{3a^{2}x^{2} } =\frac{3a\times a}{6a^{2} x^{2} } -\frac{x\times x}{6a^{2}x^{2} } +\frac{a\times 2}{6a^{2}x^{2} } =\frac{3a^{2}-x^{2}+2a }{6a^{2}x^{2} }[/tex]
