Question

Упростите выражение.

Answer 1

1\(x(x+1)) +1\((x+1)(x+2))  +1\((x+2)(x+3)) +1\((x+3)(x+4))+1\((x+4)(x+5))=


=[1\(x(x+1)) +1\((x+1)(x+2)) ]+{1\((x+2)(x+3))+1\((x+3)(x+4))+1\((x+4)(x+5))}=

=[(x+2))\(x(x+1)(x+2)))+x\(x(x+1)(x+2))]+
                                             +{1\((x+2)(x+3))+1\((x+3)(x+4))+1\((x+4)(x+5))}=

=[2(x+1)/(x(x+1)(x+2)))+1\((x+2)(x+3))]+{1\((x+3)(x+4))+1\((x+4)(x+5))}=

=[2/(x(x+2))+1\((x+2)(x+3))]+{1\((x+3)(x+4))+1\((x+4)(x+5))}=

=[2(x+3)/(x(x+2)(x+3))+x\(x(x+2)(x+3))]+{1\((x+3)(x+4))+1\((x+4)(x+5))}=

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

=[3/(x(x+3))+1\((x+3)(x+4))]+1\((x+4)(x+5))=

=[3(x+4)/(x(x+3)(x+4))+x\(x(x+3)(x+4))]+1\((x+4)(x+5))=

=4(x+3)/(x(x+3)(x+4))+1\((x+4)(x+5))=4/(x(x+4))+1\((x+4)(x+5))=

=4(x+5)/(x(x+5)(x+4))+x\(x(x+4)(x+5))=5(x+4)/(x(x+4)(x+5))=5/(x(x+5))



ответ в) 5/(x(x+5))