Úpravy výrazů 1

  1. Rozložte na součin:

    1. (x+y+r)^3 - (x+y-r)^3=
    2. 2x^4 + x^3 + 4x^2 + x + 2=
    3. t^3 + 3t^2 + 4t +2=
  2. Zjednodušte:

    1. \dfrac{6x^3+2x^2+x+5}{x+1}=
    2. \dfrac{1+5x}{1-5x}-\dfrac{1-5x}{1+5x}=
    3. \dfrac{ax-a}{x+1}-\dfrac{ax+a}{x-1}=
    4. \left(\dfrac{1}{a+1}-\dfrac{2a}{a^2-1}\right)\left(\dfrac{1}{a-1}\right)=
    5. \left(\dfrac{x-1}{x-2} - \dfrac{x}{x-1}\right)\left(x - \dfrac{3x}{x+1}\right)=
    6. \displaystyle\frac{m-n}{m^{\frac12} - n^{\frac12}}-\frac{m^{\frac32} - n^{\frac32}}{m-n} =
    7. \displaystyle \left(1+\frac{a}{a+1}\right):\left[\left(1+\frac{3a^2}{a^2-1}\right)\cdot\frac{1-2a}{1-a}\right]=
    8. \displaystyle \frac{a^2-1}{n^2+an}\left(\frac{1}{1-\frac{1}{n}}-1\right)\cdot\frac{a-an^3-n^4+n}{1-a^2}=
    9. \displaystyle \frac{\frac{1}{a-x}-\frac{1}{a-y}+\frac{x}{(a-x)^2}-\frac{y}{(a-y)^2}}{\frac{1}{(a-x)^2(a-y)}-\frac{1}{(a-y)^2(a-x)}}+a(x+y)=
    10. \displaystyle x^2y^2\left[\frac{1}{(x+y)^2}\left(\frac{1}{x^2}+\frac{1}{y^2}\right) +\frac{2}{(x+y)^2}\left(\frac{1}{x}+\frac{1}{y}\right)\right]=

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