Potrzebuję na szybko help!!!![latex] frac{x-2}{x-5}+ frac{x-3}{x-5}=2x-5 [/latex]

D: x -5 ≠ 0 x ≠ 5 D = R{5} x-2+x-3=(2x-5)(x-5) 2x-5=2x²-10x-5x+25 0 = 2x²-17x+30 f(x) = 2x²-17x+30 Δ=(-17)²+4*30*2 Δ=289-240 Δ=49 √Δ=7 [latex] x_{1} = frac{17+7}{4} = frac{24}{4} = 6[/latex] ∈ D [latex] x_{2} = frac{17-7}{4} = frac{10}{4} = 2.5[/latex] ∈ D f(x) = 0 ⇔ x ∈ {2.5;6}

[latex]frac{x-2}{x-5}+frac{x-3}{x-5} = 2x-5 |*(x-5)\\Z:\x-5 eq 0\x eq 5\\(2x-5)(x-5) = x-2+x-3\\2x^{2}-10x-5x+25=2x-5\\2x^{2}-15x-2x+25+5 = 0\\2x^{2}-17x+30 = 0\\Delta = b^{2}-4ac = 289-240 = 49\\sqrt{Delta} = 7\\x_1 = frac{-b-sqrt{Delta}}{2a}=frac{17-7}{4} = 2frac{1}2}\\x_2 = frac{-b+sqrt{Delta}}{2a} = frac{17+7}{4} = 6\\x inlbrace2frac{1}{2};6 brace[/latex]