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(x-1)(x-2)/(x+3)+(x-1)(x-3)/(x+2)=(x-2)(x-3)/(x+1),
两边都乘以(x+3)(x+2)(x+1),得
[(x-1)(x-2)(x+2)+(x-1)(x-3)(x+3)](x+1)=(x-2)(x-3)(x+2)(x+3),
(x-1)(x^2-4+x^2-9)(x+1)=(x^2-4)(x^2-9),
(x^2-1)(2x^2-13)=(x^2-4)(x^2-9),
2x^4-15x^2+13=x^4-13x^2+36,
x^4-2x^2+1=24,
x^2-1=2√6(舍弃负值),
x=土√(1+2√6).
仅供参考。
两边都乘以(x+3)(x+2)(x+1),得
[(x-1)(x-2)(x+2)+(x-1)(x-3)(x+3)](x+1)=(x-2)(x-3)(x+2)(x+3),
(x-1)(x^2-4+x^2-9)(x+1)=(x^2-4)(x^2-9),
(x^2-1)(2x^2-13)=(x^2-4)(x^2-9),
2x^4-15x^2+13=x^4-13x^2+36,
x^4-2x^2+1=24,
x^2-1=2√6(舍弃负值),
x=土√(1+2√6).
仅供参考。
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原方程两边同乘以(x-1)(x-2)(x-3)【公分母】,得到:
(x+3)(x-3)+(x+2)(x-2)=(x+1)(x-1)
==》 x²-9+x²-4=x²-1
==》 x²=12
==》 x=±2√3
(x+3)(x-3)+(x+2)(x-2)=(x+1)(x-1)
==》 x²-9+x²-4=x²-1
==》 x²=12
==》 x=±2√3
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(x-1)(x-2)/(x+3)+(x-1)(x-3)/(x+2)=(x-2)(x-3)/(x+1) ; x≠-1,-2,-3
(x-1)(x-2)(x+1)(x+2)+(x-1)(x-3)(x+1)(x+3)=(x-2)(x-3)(x+2)(x+3)
(x-2)(x-3)(x+2)(x+3)-(x-1)(x-2)(x+1)(x+2) =(x-1)(x-3)(x+1)(x+3)
(x-2)(x+2)[ (x^2-9)-(x^2-1)] =(x-1)(x-3)(x+1)(x+3)
-8(x-2)(x+2)=(x-1)(x-3)(x+1)(x+3)
-8(x-2)(x+2)=(x^2-1)(x^2-9)
-8(x-2)(x+2)=x^4-10x^2+9
-8x^2+32 =x^4-10x^2+9
x^4-2x^2-23=0
(x^2-1)^2 =24
x^2 -1 =2√6 or -2√6
x^2 = 1+2√6 or 1-2√6 (rej)
x=√(1+2√6) or -√(1+2√6)
(x-1)(x-2)(x+1)(x+2)+(x-1)(x-3)(x+1)(x+3)=(x-2)(x-3)(x+2)(x+3)
(x-2)(x-3)(x+2)(x+3)-(x-1)(x-2)(x+1)(x+2) =(x-1)(x-3)(x+1)(x+3)
(x-2)(x+2)[ (x^2-9)-(x^2-1)] =(x-1)(x-3)(x+1)(x+3)
-8(x-2)(x+2)=(x-1)(x-3)(x+1)(x+3)
-8(x-2)(x+2)=(x^2-1)(x^2-9)
-8(x-2)(x+2)=x^4-10x^2+9
-8x^2+32 =x^4-10x^2+9
x^4-2x^2-23=0
(x^2-1)^2 =24
x^2 -1 =2√6 or -2√6
x^2 = 1+2√6 or 1-2√6 (rej)
x=√(1+2√6) or -√(1+2√6)
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(x-1)(x-2)/(x+3)+(x-1)(x-3)/(x+2)=(x-2)(x-3)/(x+1),
两边都乘以(x+3)(x+2)(x+1),得
[(x-1)(x-2)(x+2)+(x-1)(x-3)(x+3)](x+1)=(x-2)(x-3)(x+2)(x+3),
(x-1)(x^2-4+x^2-9)(x+1)=(x^2-4)(x^2-9),
(x^2-1)(2x^2-13)=(x^2-4)(x^2-9),
2x^4-15x^2+13=x^4-13x^2+36,
x^4-2x^2+1=24,
x^2-1=2√6(舍弃负值),
x=土√(1+2√6).
仅供参考。
两边都乘以(x+3)(x+2)(x+1),得
[(x-1)(x-2)(x+2)+(x-1)(x-3)(x+3)](x+1)=(x-2)(x-3)(x+2)(x+3),
(x-1)(x^2-4+x^2-9)(x+1)=(x^2-4)(x^2-9),
(x^2-1)(2x^2-13)=(x^2-4)(x^2-9),
2x^4-15x^2+13=x^4-13x^2+36,
x^4-2x^2+1=24,
x^2-1=2√6(舍弃负值),
x=土√(1+2√6).
仅供参考。
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