解方程:(8x+24)/(x^2+6x+9)+x^2/(x^2-9)=(x^2-9)/(x^2-6x+9) 1/(x-7)+1/(x-4)=1/(x-5)+1/(x-6)a为何值时,方程x/(x-3)=2+a/(x-3)会产生增根?(1) (8x+24)/(x^2+6x+9)+x^2/(x^2-9)=(x^2-9)/(x^2-6x+9)(2) 1/(x-7)+1/(x-4)=1/(x-5)+1/(x-6)(3
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![解方程:(8x+24)/(x^2+6x+9)+x^2/(x^2-9)=(x^2-9)/(x^2-6x+9) 1/(x-7)+1/(x-4)=1/(x-5)+1/(x-6)a为何值时,方程x/(x-3)=2+a/(x-3)会产生增根?(1) (8x+24)/(x^2+6x+9)+x^2/(x^2-9)=(x^2-9)/(x^2-6x+9)(2) 1/(x-7)+1/(x-4)=1/(x-5)+1/(x-6)(3](/uploads/image/z/379947-3-7.jpg?t=%E8%A7%A3%E6%96%B9%E7%A8%8B%3A%288x%2B24%29%2F%28x%5E2%2B6x%2B9%29%2Bx%5E2%2F%28x%5E2-9%29%3D%28x%5E2-9%29%2F%28x%5E2-6x%2B9%29+1%2F%EF%BC%88x-7%29%2B1%2F%28x-4%29%3D1%2F%28x-5%29%2B1%2F%28x-6%29a%E4%B8%BA%E4%BD%95%E5%80%BC%E6%97%B6%2C%E6%96%B9%E7%A8%8Bx%2F%28x-3%29%3D2%2Ba%2F%28x-3%29%E4%BC%9A%E4%BA%A7%E7%94%9F%E5%A2%9E%E6%A0%B9%3F%EF%BC%881%EF%BC%89+%288x%2B24%29%2F%28x%5E2%2B6x%2B9%29%2Bx%5E2%2F%28x%5E2-9%29%3D%28x%5E2-9%29%2F%28x%5E2-6x%2B9%29%EF%BC%882%EF%BC%89+1%2F%EF%BC%88x-7%29%2B1%2F%28x-4%29%3D1%2F%28x-5%29%2B1%2F%28x-6%29%EF%BC%883)
解方程:(8x+24)/(x^2+6x+9)+x^2/(x^2-9)=(x^2-9)/(x^2-6x+9) 1/(x-7)+1/(x-4)=1/(x-5)+1/(x-6)a为何值时,方程x/(x-3)=2+a/(x-3)会产生增根?(1) (8x+24)/(x^2+6x+9)+x^2/(x^2-9)=(x^2-9)/(x^2-6x+9)(2) 1/(x-7)+1/(x-4)=1/(x-5)+1/(x-6)(3
解方程:(8x+24)/(x^2+6x+9)+x^2/(x^2-9)=(x^2-9)/(x^2-6x+9) 1/(x-7)+1/(x-4)=1/(x-5)+1/(x-6)
a为何值时,方程x/(x-3)=2+a/(x-3)会产生增根?
(1) (8x+24)/(x^2+6x+9)+x^2/(x^2-9)=(x^2-9)/(x^2-6x+9)
(2) 1/(x-7)+1/(x-4)=1/(x-5)+1/(x-6)
(3) a为何值时,方程x/(x-3)=2+a/(x-3)会产生增根?
解方程:(8x+24)/(x^2+6x+9)+x^2/(x^2-9)=(x^2-9)/(x^2-6x+9) 1/(x-7)+1/(x-4)=1/(x-5)+1/(x-6)a为何值时,方程x/(x-3)=2+a/(x-3)会产生增根?(1) (8x+24)/(x^2+6x+9)+x^2/(x^2-9)=(x^2-9)/(x^2-6x+9)(2) 1/(x-7)+1/(x-4)=1/(x-5)+1/(x-6)(3
(1)原方程化为 8(x+3)/[(x+3)²]+x²/[(x+3)(x-3)]=[(x+3)(x-3)]/[(x-3)²]
则 8/(x+3)+x²/[(x+3)(x-3)]=(x+3)/(x-3)
两边同时乘 (x+3)(x-3),得 8(x-3)+x²=(x+3)²,即 8x-24+x²=x²+6x+9
解得 x=33/2
(2)两边分别通分,得 (2x-11)/[(x-7)(x-4)]=(2x-11)/[(x-6)(x-5)]
则 (2x-11){1/[(x-7)(x-4)]-1/[(x-6)(x-5)]}=0
所以 2x-11=0 或 1/[(x-7)(x-4)]-1/[(x-6)(x-5)]=0
解得 x=11/2 或 无解
(3)方程的增根只可能是 x=3,
原方程两边乘 (x-3) 得 x=2(x-3)+a
代入 x=3 ,得 3=a
故 a=3