Question

解方程(X-2)/(X+3)=1-(2X-13)/(X^2-9)

Answer 1

(X+1)/(X-1)+ 4/(X^2-1)=1 1/(2-X)=1/(X-2) - (6-X)/(3X^2-12)

[(X+1)^2+4]/(X^2-1)=1

X^2+2X+1+4=X^2-1

2X=-6

X=3

分式要检验

经检验,成立

1/(2-X)=1/(X-2) - (6-X)/(3X^2-12)

-1/(X-2)=1/(X-2) - (6-X)/[3(X+2)(X-2)]

-2/(X-2)=- (6-X)/[3(X+2)(X-2)]

2/(X-2)= (6-X)/[3(X+2)(X-2)]

6(X+2)(X-2)=(6-X)(X-2)

6X^2-24=-X^2+8X-12

7X^2-8X-12=0

X=2,X=-6/7

经检验,X=2是增根

X=-6/7