Question

第3步往后的过程

从第3步往后的具体步骤

Answer 1

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