Úpravy výrazů 1 | Studijní materiály

Rozložte na součin:
1. $(x+y+r)^3 - (x+y-r)^3=$
2. $2x^4 + x^3 + 4x^2 + x + 2=$
3. $t^3 + 3t^2 + 4t +2=$
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. $\displaystyle x^2y^2\left[\frac{1}{(x+y)^2}\left(\frac{1}{x^2}+\frac{1}{y^2}\right) +\frac{2}{(x+y)^2}\left(\frac{1}{x}+\frac{1}{y}\right)\right]=$