Question

x+2/x+1-x+3/x+2-x-4/x-3+x-5/x-4如何分解因式

Answer 1

原式=(x+2)/(x+1)-(x+3)/(x+2)-（x-4)/(x-3)+(x-5)/(x-4)

=[(x+2)*(x+2)-(x+3)*（x+1）]/(x+1)*(x+2)--[(x-4)*(x-4)-(x-3)*(x-5)]/(x-3)*(x-4)

=1/(x+1)*(x+2)-1/(x-3)*(x-4)

=[(x-3)*(x-4)-(x+1)*(x+2)]/[(x+1)*(x+2)*(x-3)*(x-4)]

=10(1-x)/[(x+1)*(x+2)*(x-3)*(x-4)]