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2010-03-30T19:20:01+02:00
C)
x²+8x-2/x²+2x-8 + x/x+4 = x+1/x+2
D: x∈R/{-4;2}
x²+8x-2/(x+4)(x-2) + x/x+4 = x+1/x+2 /×(x+4)(x-2)
x²+8x-2 + x²-2x = x²+4x+x+4
x²+6x-2 = 5x+4
x²+x-6 = 0
Δ=1²-4×(-6)×1
Δ=25
√Δ=5
x1=-1-5/2 = -3
x2=-1+5/2 = 2

d)
x+1/x-3 + x-2/x+1 = x²+x+12/x²-2x-3
D: x∈R/{3;-1}
x+1/x-3 + x-2/x+1 = x²+x+12/(x+1)(x-3) /(x+1)(x-3)
x²+x+x+1 +x²-3x-2x+6 = x²+x+12
x²-3x+7 = x+12
x²-2x-5 = 0
Δ=(-4)²-4×(-5)×1
Δ=36
√Δ=6
x1=4-6/2 = 1
x2=4+6/2 = 5