Question

已知X+1/X=2,求分式X^2+X+1/(3X^2-5X+3)的值

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Answer 1

解：x+1/x=2
X²+1=2X 或 x+1/x=1+1/御则掘1
X²-2X+1=0 x=1
(X-1)²=0
X=1
代入：
(1+1+1)/(3-5+3)=3
原式盯旦=3
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Answer 2

同时处以x，汪培得出(X^2+X+1)/(3X^2-5X+3)=（x+1+1/x)/困键唯(3x-5+3/x）亮腊=（2+1）/（3x2-5）=3/1=3

Answer 3

X+1/樱烂宴X=2
(X^2+1)/历棚X=2
则 X^2=2X-1
X^2+X+1/脊银(3X^2-5X+3)
=2X-1+X+1/(6X-3-5X+3)
=X-1+1/X
=X+1/X-1
=2-1
=1

Answer 4

X+1/X=2,(X-1)^2=0,X=1
X^2+X+1/(3X^2-5X+3)=3