Question

x+7除以x+6 加 x+9除以x+8=x+10除以x+9 加 x+6除以 x+5

Answer 1

(x+7)/(x+6)+(x+9)/(x+8)=(x+10)/(x+9)+(x+6)/(x+5)

(x+9)/(x+8)-(x+10)/(x+9)=(x+6)/(x+5)-(x+7)/(x+6)

[(x+9)²-(x+8)(x+10)]/[(x+8)*(x+9)]=[(x+6)²-(x+5)(x+7)]/[(x+5)(x+6)]

(x²+18x+81-x²-18x-80)/[(x+8)(x+9)]=(x²+12x+36-x²-12x-35)/[(x+5)(x+6)]

1/[(x+8)(x+9)]=1/[(x+5)(x+6)]

(x+5)(x+6)=(x+8)(x+9)

x²+11x+30=x²+17x+72

6x=-42

x=-7

经检验,x=-7是原方程的解