Odpowiedź:
Zad 9
a)
[tex] \frac{x - 2}{ {x}^{2} } \times \frac{3x}{2x - 4} = \frac{3 {x}^{2} - 6x}{2 {x}^{3} - 4 {x}^{2} } = \frac{3x(x - 2)}{2 {x}^{2}(x - 2) } = \frac{3x}{2 {x}^{2} } = \frac{3}{2x} [/tex]
Dziedzina:
x²≠0 i 2x-4≠0
x≠2
x€R\{2}
b)
[tex] \frac{ {x}^{2} }{3 - x} \times \frac{3x - 9}{ {x}^{4} } = \frac{3 {x}^{3} - 9 {x}^{2} }{3 {x}^{4} - {x}^{5} } = \frac{3 {x}^{2} (x - 3)}{ - {x}^{4} (x - 3)} = \frac{3 {x}^{2} }{ - {x}^{4} } = \frac{3}{ - {x}^{2} } [/tex]
Dziedzina:
3-x≠0 i x⁴≠0
x≠3. x≠0
x€R\{0,3}
c)
[tex] \frac{4 {x}^{2} - 16 }{6 - 3x} \times \frac{ {x}^{2} }{4x + 8} = \frac{4 {x}^{4} - 16 {x}^{2} }{ - 12 {x}^{2} + 48} = \frac{4 {x}^{2}( {x}^{2} - 4) }{ - 12( {x}^{2} - 4) } = \frac{4 {x}^{2} }{ - 12} = \frac{ {x}^{2} }{ - 3} [/tex]
Dziedzina:
6-3x≠0 i 4x+8≠0
x≠2 i x≠-2
x€R\{-2,2}
Zad 11
a)
[tex] \frac{3}{4x} \div \frac{x - 1}{6x} = \frac{3}{4x} \times \frac{6x}{x - 1} = \frac{3 \times 3}{2x - 2} = \frac{9}{2x - 2} [/tex]
Dziedzina:
4x≠0 i 6x≠0 i (x-1)/6x≠0
x≠0 i x-1≠0 i 6x≠0
x≠1
x€R\{0,1}
b)
[tex] \frac{10x + 2}{ {x}^{2} } \div \frac{5x + 1}{x} = \frac{10x + 2}{ {x}^{2} } \times \frac{x}{5x + 1} = \frac{10x + 2}{5 {x}^{2} + x} = \frac{2(5x + 1)}{x(5x + 1)} = \frac{2}{x} [/tex]
Dziedzina:
x²≠0 i x≠0 i (5x+1)/x≠0
x≠0 i 5x+1≠0 i x≠0
x≠-⅕
x€R\{-⅕,0)
c)
[tex] \frac{ {x}^{3} }{6x - 2} \div \frac{2x}{1 - 3x} = \frac{ {x}^{3} }{6x - 2} \times \frac{1 - 3x}{2x} = \frac{ {x}^{2} (1 - 3x)}{ - 4(1 - 3x)} = \frac{ {x}^{2} }{ - 4} [/tex]
Dziedzina:
6x-2≠0 i 1-3x≠0 i 2x/(1-3x)≠0
x≠⅓ i 2x≠0 i 1-3x≠0
x≠0
x€R\{0,⅓}
