8.
a)
Zał:
2x ≠ 0 ⇒ x ≠ 0
x² - 2x = x(x - 2) ⇒ x ≠ 0 ∧ x ≠ 2
D = R \ {0, 2}
[tex]\frac{x-5}{2x} - \frac{x-2}{x^{2}-2x} = \frac{x-5}{2x} - \frac{x-2}{x(x-2)} = \frac{x-5}{2x} - \frac{1}{x} = \frac{x-5-2}{2x} = \frac{x-7}{2x}[/tex]
b)
Zał:
x² + 4 ≥ 0
x ≠ 0
D = R \ {0}
[tex]\frac{3x+3}{x^{2}+4} :\frac{x+1}{x} = \frac{3(x+1)}{x^{2}+4}\cdot\frac{x}{x+1} = \frac{3x}{x^{2}+4}[/tex]
