Question

方程(x-1/x-2)-(x-3/x-4)=(x-2/x-3)-(x-4/x-5)解为x=7/2,(1/x-7)-(1/x-5)=(1/x-6)-(1/x-4)解为x=11/2

求方程(1/x-7)+(1/x-1)=(1/x-6)+(1/x-2)的解
和方程(1/x+a)-(1/x+b)=(1/x+c)-(1/x+d)的解(a,b,c,d表示不同的数,且a+d=b+c)

Answer 1

(1/x-7)+(1/x-1)=(1/x-6)+(1/x-2)
1/(X-7)-1/(X-6)=1/(X-2)-1/(X-1)
(X-6-X+7)/[(X-7)(X-6)]=(X-1-X+2)/[(X-1)(X-2)]
X方-3X+2=X方-13X+42
10X=40
X=4

(1/x+a)-(1/x+b)=(1/x+c)-(1/x+d)
(X+B-X-A)/[(X+A)(X+B)]=(X+D-X-C)/[(X+C)(X+D)]
B-A=D-C
X方+(A+B)X+AB=X方+(C+D)X+CD
X=(CD-AB)/(A+B-C-D)

Answer 2

1/(x-7)-1/(x-5)=1/(x-6)-1/(x-4)
[(x-5)-(x-7)]/[(x-5)*(x-7)]=[(x-4)-(x-6)]/[(x-4)*(x-6)]
2/(x^2-12x+35)=2/(x^2-10x+24)
x^2-12x+35=x^2-10x+24
-2x+11=0
x=11/2