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共回答了21个问题采纳率:95.2% 举报
(1)1/(x-2)+k/(x+2)=4/(x²-4),
(x+2+kx-2k)/(x+2)(x-2)=4/(x+2)(x-2)
∴x+kx+2-2k=4
x(1+k)=2(1+k)
当k+1=0,即k=-1时,有增根x=2(不是x=-2)
(2)(m+n)/(2m-2n)-2mn/(m²-n²)
=[(m+n)²-4mn]/2(m-n)(m+n)
=(m-n)²/2(m-n)(m+n)
=(m-n)/2(m+n)..
(3)1/(1+x)+1/(1+x)+2/(1+x²)+4/(1+x^4)
=2/(1-x²)+2/(1+x²)+4/(1+x^4)
=4/(1-x^4)+4/(1+x^4)
=8/(1-x^8).
(4)①(x+1)/(x-1)-4/(x²-1)=1
x²+2x+1-4)=x²-1
x=1(分母为0,无解)
②(1-3x)/(1+3x)+(3x+1)/(3x-1)=12/(1-9x²)
(1-6x+9x²-1-6x-9x²)/(1+3x)(1-3x)=12/(1+3x)(1-3x)
-12/(1+3x)(1-3x)=12/(1+3x)(1-3x)
∵-12≠12(无解)
(5)1/(a²+1)+1/(b²+1)
=(b²+1+a²+1)/(a²+1)(b²+1)
=(a²+b²+2)/(a²b²+a²+b²+1)
=(a²+b²+2)/(a²+b²+2)
=1
1年前
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