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mrshaurman
@mrshaurman
March 2022
2
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решите неравенство:
2/(х+1)-1/(х-1)<1
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juniorotabekpai8do
Решение внизу на фото
2 votes
Thanks 2
cocirmariadenis
2/x+1-1/x-1<1, x≠-1; x≠1
2/x+1-1/x-1-1<0
2(x-1)-(x+1)*(x-1)/(x+1)*(x-1)<0
2x-2-x-1-(x²-1)/(x+1)*(x-1)<0
2x-2-x-1-x²+1/(x+1)*(x-1)<0
x-2-x²(x+1)*(x-1)<0
{x-2-x²<0
{(x+1)*(x-1)>0
{x-2-x²>0
{(x+1)*(x-1)<0
}x∈R
}x∈[-∞, -1] ∪ [1, +∞]
}x∈∅
x∈[-1, 1
x∈ [-∞, -1) ∪ [ 1, +∞] x≠-1, x≠1
0 votes
Thanks 0
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Answers & Comments
Решение внизу на фото
2/x+1-1/x-1-1<0
2(x-1)-(x+1)*(x-1)/(x+1)*(x-1)<0
2x-2-x-1-(x²-1)/(x+1)*(x-1)<0
2x-2-x-1-x²+1/(x+1)*(x-1)<0
x-2-x²(x+1)*(x-1)<0
{x-2-x²<0
{(x+1)*(x-1)>0
{x-2-x²>0
{(x+1)*(x-1)<0
}x∈R
}x∈[-∞, -1] ∪ [1, +∞]
}x∈∅
x∈[-1, 1
x∈ [-∞, -1) ∪ [ 1, +∞] x≠-1, x≠1