# Field acioms- division

• November 15th 2007, 03:03 PM
lds09
Field acioms- division
Hello, I need some help on how to prove this using the field axioms of the real numbers

Given a and b with a =/ 0, there is exactly one x such that ax = b. This x is denoted as b/a.

$ax=b$ then $a^{-1}(ax)=a^{-1}b$ then $(a^{-1}a)x=a^{-1}b$ thus $1x = a^{-1}b$ thus $x=a^{-1}b$.