Korzystając z własności proporcji, rozwiąż równanie: a[latex]frac{1}{3x}=frac{2x-3}{2x}[/latex]   b[latex]frac{4x-3}{2x-3}=frac{5x-3}{x+1}[/latex]   c[latex]frac{x-6}{x-5}=frac{2x-11}{x-1}[/latex]

a) 1/3x = (2x-3)/2x                                                Z: x ≠ 0                                                                         D = R {0} 3x(2x-3) = 2x 6x²-9x = 2x 6x²-9x-2x = 0 6x²-11x = 0 x(6x-11) = 0 x = 0  ∉ D 6x-11 = 0 6x = 11  /:6 x = 11/6 x = 1⅚ Odp. x = 1⅚   b) (4x-3)/(2x-3) = (5x-3)/(x+1)                             Z: x+1 ≠ 0                                 x ≠ -1                                2x-3 ≠ 0                                  x ≠ 1½                              D = R {-1;1½}   (2x-3)(5x-3) = (4x-3)(x+1) 10x²-6x-15x+9 = 4x²+4x-3x-3 10x²-21x+9 = 4x²+x-3 10x²-4x²-21x-x+9+3 = 0 6x²-22x+12 = 0  /:2 3x²-11x+6 = 0 Δ = 121-72 = 49 √Δ = √49 = 7  x1 = (11-7)/6 = 2/3 x2 = (11+7)/6 = 3 Odp. x = 2/3   v   x = 3   c) (x-6)/(x-5) = (2x-11)/(x-1)                             Z: x-1 ≠ 0                                 x ≠ 1                                 x-5 ≠ 0                                 x ≠ 5                             D = R {1;5} (x-5)(2x-11) = (x-1)(x-6) 2x²-11x-10x+55 = x²-6x-x+6 2x²-21x+55 = x²-7x+6   2x²-x²-21x+7x+55-6 = 0 x²-14x+49 = 0 Δ = 196-196 = 0 x = 14/2 = 7 Odp. x = 7                                                                                                                                                                                                                                                                                                                                                                                 

Rozwiąż równanie korzystając z własności proporcji.       a)  [latex]frac{x-3}{5}=frac{2x-3}{4}[/latex]   b)  [latex]frac{x+1}{-2}=frac{x-1}{4}[/latex]   c)  [latex]frac{-5}{3x-4}=frac{10}{2x+5}[/latex]   d)  [latex]frac{x-6}{x-3}=frac{x-4}{x+1}[/latex]

Rozwiąż równanie korzystając z własności proporcji.       a)  [latex]frac{x-3}{5}=frac{2x-3}{4}[/latex]   b)  [latex]frac{x+1}{-2}=frac{x-1}{4}[/latex]   c)  [latex]frac{-5}{3x-4}=frac{10}{2x+5}[/latex]   d)  [latex]frac{x-6}{x-3}=f...