ax+x/(x-1)如何推出ax+1+1/(x-1)如何推出a(x-1)+1/(x-1)+

ax+x/(x-1)
减去(x-1)/(x-1)再加上 (x-1)/(x-1) 也就是1
ax + [x / (x - 1) - (x - 1) / (x - 1)] + 1
= ax + 1 + 1 / (x - 1)

然后减去a再加上a
ax + 1 + 1 / (x - 1) - a + a
=ax - a + 1 + 1 / (x - 1) + a
前两项提公因式
=a(x - 1) + 1 / (x - 1) + a + 1

ax+x/(x-1)
=ax+[(x-1)+1]/(x-1)
=ax+(x-1)/(x-1)+1/(x-1)
=ax+1+1/(x-1)
=a[(x-1)+1]+1+1/(x-1)
=a(x-1)+1+a+1/(x-1)
=a(x-1)+1/(x-1)+a+1

利用乘法和除法的分配率

如何推出ax+1+1/(x-1)
ax+x/(x-1)
=ax+((x-1)+1)/(x-1)--------->其中((x-1)+1)/(x-1)即(x-1)/(x-1)+1/(x-1)也就是1+1/(x-1)

如何推出a(x-1)+1/(x-1)+a+1
ax+x/(x-1)上一步得出=ax+1+1/(x-1)其中ax=a(x-1)+a 故