Question

1.Aflaţi DVA al raportului:
a)$\frac{1}{x-2}$
b)$\frac{a}{ a^{2}-4 }$
2.Efectuaţi:
a)$\frac{x}{2y}+ \frac{y}{2y}$
b)$\frac{m}{2m+2n} +1$
3.Aduceţi la forma cea mai simplă:
a)$\frac{2}{5x} + \frac{3}{5x} - \frac{24}{10x}$
b)$\frac{5x+1}{2y} + \frac{7-3x}{2y} - \frac{4x-1}{4y}$

Answer 1

1.a)  
x - 2 = 0    =>   x = 2 
=> DVA = R - {2}

1.b)
 a² - 4 = 0
 (a - 2)(a + 2) = 0   
a - 2 = 0      => a₁ = 2
a + 2  = 0    => a₂ = - 2
=> DVA = R - {-2; 2}
  2.a)
$\frac{x}{2y}+ \frac{y}{2y} = \frac{x+y}{2y} \\ \\ 2.b) \\ \frac{m}{2m+2n} +1= \frac{m}{2m+2n} + \frac{2m+2n}{2m+2n} =\frac{m+2m+2n}{2m+2n}=\frac{3m+2n}{2m+2n}$

3.a)
$\frac{2}{5x} + \frac{3}{5x} - \frac{24}{10x} = \frac{4}{10x} + \frac{6}{10x} - \frac{24}{10x} =\frac{4+6-24}{10x}=\frac{-14}{10x}=\frac{-7}{5x}$

3.b)
$\frac{5x+1}{2y} + \frac{7-3x}{2y} - \frac{4x-1}{4y}= \\ \\ =\frac{2(5x+1)}{4y} + \frac{2(7-3x)}{4y} - \frac{4x-1}{4y}= \\ \\ =\frac{10x+2}{4y} + \frac{14-6x}{4y} - \frac{4x-1}{4y}= \\ \\ =\frac{10x+2+14-6x-4x+1}{4y}= \\ \\ =\frac{0x+17}{4y}=\frac{17}{4y}$