一元二次方程式問題

(x+9)/(x+8)＋(x+7)/(x+6)＝(x+10)/(x+9)＋(x+6)/(x+5)
==> 1＋1/(x+8)＋1＋1/(x+6)＝1＋1/(x+9)＋1＋1/(x＋5)
==> 1/(x+6)－1/(x+9)＝1/(x+5)－1/(x＋8)
==> (x＋9－x－6)/(x+6)(x+9)＝(x＋8－x－5)/(x+5)(x＋8)
==> (x+6)(x+9)＝(x+5)(x＋8)
==> x^2＋15x＋54＝x^2＋13x＋40
==> 2x＝-14
==> x＝-7

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ＴＳ７７７。ＣＣ

(X+9)/(X+8) +(X+7)/(X+6) = (X+10)/(X+9) +(X+6)(X+5)
[1+1/(X+8)] + [1+1/(X+6)] = [1+1/(X+9)] + [1+1/(X+5)]
1/(X+8) +1/(X+6) = 1/(X+9) +1/(X+5)

令A=X+7，則1/(A+1) +1/(A-1) = 1/(A+2) +1/(A-2)
2A/(A^2 -1) = 2A/(A^2 -4)，A/(A^2 -1) = A/(A^2 -4)
A[1/(A^2 -1) -1/(A^2 -4)] =0

(1)0=A=X+7，X=-7
(2)1/(A^2 -1) -1/(A^2 -4) =0
1/(A^2 -1) = 1/(A^2 -4)
A^2 -1 = A^2 -4，impossible

ANS：-7

(x+9)/(x+8)+(x+7)/(x+6)=(x+10)/(x+9)+(x+6)/(x+5)
(x+6)(x+9)(x+5)(x+9)+(x+7)(x+8)(x+9)(x+5)=(x+10)(x+8)(x+6)(x+5)
+(x+6)(x+8)(x+6)(x+9)
(x+6)(x+9)(x+5)(x+9)－(x+10)(x+8)(x+6)(x+5)
=(x+6)(x+8)(x+6)(x+9)－(x+7)(x+8)(x+9)(x+5)
(x+6)(x+5)[(x+9)(x+9)－(x+10)(x+8)]=(x+8)(x+9)[(x+6)(x+6)－(x+7)(x+5)]
(x+6)(x+5)(x^2+18x+81－x^2－18x－80)
=(x+8)(x+9)(x^2+12x+36－x^2－12x－35)
(x+6)(x+5)(x^2+1)=(x+8)(x+9)(x^2+1)
(x^2+1)[(x^2+11x+30)－(x^2+17x+72)]=0
(x^2+1)(－6x－42)=0
6x+42=0
x=－7