a) [latex] frac{3}{2x-1} + frac{3}{2x+1} [/latex] założenia [latex]2x-1 eq 0[/latex] [latex]2x eq 1 |:2 [/latex] [latex]x eq frac{1}{2} [/latex] i [latex]2x+1 eq 0 [/latex] [latex]2x eq -1 |:2 [/latex] [latex]x eq -frac{1}{2} [/latex] [latex]frac{3*(2x+1)}{(2x-1)*(2x+1)} + frac{3*(2x-1)}{(2x+1)*(2x-1)} = frac{6x+3+6x-3}{(2x+1)*(2x-1)} = frac{12x}{(2x+1)*(2x-1)}[/latex] [latex]frac{12*(-2)}{(2*(-2)+1)*(2*(-2)-1)} = frac{-24}{(-4+1)*(-4-1)} = frac{-24}{(-3)*(-5)} = frac{-24}{-15} = 1 frac{9}{15} = 1 frac{3}{5} [/latex] b) [latex] frac{x}{x-4} - frac{x}{4+x} [/latex] założenia: [latex]x-4 eq 0[/latex] [latex]x eq 4[/latex] i [latex]4+x eq 0[/latex] [latex]x eq -4[/latex] [latex]frac{x*(x+4)}{(x-4)*(x+4)} - frac{x*(x-4)}{(4+x)*(x-4)} = frac{x^{2}+4x-x^{2}+4x }{(4+x)*(x-4)} = frac{8x}{(4+x)*(x-4)} [/latex] [latex]frac{8*(-2)}{(4+(-2))*(-2-4)} = frac{-16}{(4-2)*(-6)} = frac{-16}{(2)*(-6)} = frac{-16}{-12} = 1 frac{4}{12} = 1 frac{1}{3} [/latex]
