Odpowiedź:
Zad. 1
[tex]f(x) = \sqrt{-4+5n}[/tex]
D:
[tex]-4+5n \geq 0\\5n \geq 4 \\n \geq \frac{4}{5}[/tex]
[tex]f(x) = \frac{9x^2-1}{4x^2}[/tex]
D:
[tex]4x^2 \neq 0\\x \neq 0[/tex]
Zad. 2
[tex]\frac{x^2-4}{2x^2} * \frac{4x}{x+2} = \frac{4x(x-2)(x+2)}{2x^2(x+2)} = \frac{4x^2 -8}{2x^2}= \frac{4(x^2-2)}{2x^2} = \frac{2(x^2-2)}{x^2}[/tex]
Zad. 3
[tex]\frac{25x^2 -1}{x^2-4} : \frac{5x^2+x}{2x+4} = \frac{25x^2 -1}{x^2-4}* \frac{2x+4}{5x^2+x} = \frac{(5x-1)(5x+1)}{(x-2)(x+2)} * \frac{2(x+2)}{x(5x+1)} = \frac{(5x-1)}{(x-2)} * \frac{2}{x} = \frac{10x -2 }{x^2 -2x }[/tex]
