a) Dziedzina

$x-2\ne 0$

$D=\mathbb{R}\backslash \left\{2\right\}$   

 

$\frac{x+3}{\cancel{x-2}}\cdot \cancel{\left(x-2\right)}=x+3$  

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b) Dziedzina

$x^2-9=0$  

$\left(x-3\right)\left(x+3\right)=0$  

$x=3\text{lub}x=-3$  

$D=\mathbb{R}\backslash \left\{-3,3\right\}$  

$\frac{x+4}{x^2-9}\cdot \left(x+3\right)=\frac{x+4}{\cancel{\left(x+3\right)}\left(x-3\right)}\cdot \cancel{\left(x+3\right)}=\frac{x+4}{x-3}$  

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c) Dziedzina

$3x+6=0$  

$x=-2$  

$D=\mathbb{R}\backslash \left\{-2\right\}$  

 

$\frac{x-1}{3x+6}\cdot \left(x+2\right)=\frac{x-1}{3\cancel{\left(x+2\right)}}\cdot \cancel{\left(x+2\right)}=\frac{x-1}{3}$  

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d) Dziedzina

$16-x^2=0$  

$\left(4-x\right)\left(4+x\right)=0$  

$x=4\text{lub}x=-4$  

$D=\mathbb{R}\backslash \left\{-4,4\right\}$  

 

$\frac{x^2+3}{16-x^2}\cdot \left(x+4\right)=\frac{x^2+3}{\left(4-x\right)\cancel{\left(x+4\right)}}\cdot \cancel{\left(x+4\right)}=\frac{x^2+3}{4-x}$  

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e) Dziedzina

$x^2+x+1=0$  

$\Delta =1^2-4\cdot 1\cdot 1=-3<0$   

$D=\mathbb{R}$  

 

$\frac{4}{x^2+x+1}\cdot \left(x^3-1\right)=\frac{4}{\cancel{\left(x^2+x+1\right)}}\cdot \cancel{\left(x^2+x+1\right)}\left(x-1\right)=4x-4$  

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f) Dziedzina

$x^2+8x+16=0$  

${\left(x+4\right)}^2=0$  

$x+4=0$  

$D=\mathbb{R}\backslash \left\{-4\right\}$  

 

$\frac{7x+2}{x^2+8x+16}\cdot \left(x^2-16\right)=\frac{7x+2}{\left(x+4\right)\cancel{\left(x+4\right)}}\cdot \cancel{\left(x+4\right)}\left(x-4\right)=\frac{7x^2-26x-8}{x+4}$