(x³ - 6x² + 11x - 6) : (x² - 5x + 6) = x -1 [4 /(x - 2)] - [5 /(x + 2)] = 20 / (x² - 4) [4 × (x + 2) - 5 × (x - 2)] /(x - 2)(x + 2) = 20 / (x² - 4) / × (x²-4) 4x + 8 - 5x + 10 = 20 -x = 2 x = -2 (x² + 7x + 12) / (x² - 1) > 0 D = R {-1; 1} (x² + 7x + 12)(x² - 1) / (x² -1)(x² - 1) > 0 (x² + 7x + 12)(x - 1)(x + 1) > 0 x₁ = -4 x₂ = -3 x₃ = 1 x₃ ∉ D x₄ = -1 x₄ ∉ D x∈( - ∞; -4) i (-3; -1)
1)x³-6x²+11x-6/(x²-5x+6)=x-1 -x³+5x²-6x ___________ = -x²+5x-6 x²-5x+6 ____________ = = = To jest kompletne dzielenie wielomianów 2)4/x-2-5/x+2=20/x²-4 4*(x+2)-5(x-2)/x²-4=20/x²-4 4x+8-5x+10/x²-4=20/x²-4 -x+18/x²-4-20/x²-4=0 -x-2/x²-4=0 (-x-2)(x²-4)=0 pierwiastek podwójny→(x=-2)∨x=2 3)x²+7x+12/x²-1>0 (x²+7x+12)(x²-1)>0 Δ=7²-4*1*12 x²=1 =49-48=1 x₃=1∨x₄=-1 pierw.zΔ=1 x₁=-7-1/2=-4 x₂=-7+1/2=-3 x∈(-4;-3)∨(-1;1)
w zał za moment
