解方程1\x^+3x+2 + 1\x^2+5x+6 + 1\x^2+7x+12 + 1\x^2+x=4/21的解是
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解方程1\x^+3x+2 + 1\x^2+5x+6 + 1\x^2+7x+12 + 1\x^2+x=4/21的解是
![解方程1\x^+3x+2 + 1\x^2+5x+6 + 1\x^2+7x+12 + 1\x^2+x=4/21的解是](/uploads/image/z/3642245-53-5.jpg?t=%E8%A7%A3%E6%96%B9%E7%A8%8B1%5Cx%5E%2B3x%2B2+%2B+1%5Cx%5E2%2B5x%2B6+%2B+1%5Cx%5E2%2B7x%2B12+%2B+1%5Cx%5E2%2Bx%3D4%2F21%E7%9A%84%E8%A7%A3%E6%98%AF)
1/(x^2+3x+2)+1/(x^2+5x+6)+1/(x^2+7x+12)+1/(x^2+x)=4/21
1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+1/x(x+1)=4/21
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)=4/21
1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)=4/21
1/x-1/(x+4)=4/21
(x+4-x)/x(x+4)=4/21
4/x(x+4)=4/21
1/x(x+4)=1/21
x(x+4)=21
x^2+4x-21=0
(x+7)(x-3)=0
x=-7或x=3
经检验x=-7或x=3是方程的解
再问: 方程1/x-1+2/x-2=1的解的个数是
1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+1/x(x+1)=4/21
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)=4/21
1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)=4/21
1/x-1/(x+4)=4/21
(x+4-x)/x(x+4)=4/21
4/x(x+4)=4/21
1/x(x+4)=1/21
x(x+4)=21
x^2+4x-21=0
(x+7)(x-3)=0
x=-7或x=3
经检验x=-7或x=3是方程的解
再问: 方程1/x-1+2/x-2=1的解的个数是
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