Question 257942
Solve for x. 
{{{abx-b=ax-1}}}
<pre><font size = 4 color = "indigo"><b>
Get all the terms that have x in them on one side and
all the terms that don't have x in them on the other side:

{{{abx-ax=b-1}}}

Factor out x, the letter you are solving for:

{{{x(ab-a)=b-1}}}

Divide both sides by {{{(ab-a)}}}

{{{x(ab-a)/(ab-a)=(b-1)/(ab-a)}}}

{{{x(cross(ab-a))/(cross(ab-a))=(b-1)/(ab-a)}}}

{{{x=(b-1)/(ab-a)}}}

But you aren't finished yet because you can
factor a out of the denominator on the right:

{{{x=(b-1)/(a(b-1))}}}

Then cancel:

{{{x=(cross(b-1))/(a(cross(b-1)))}}}

{{{x=1/a}}}  

Be sure you realize that you don't get {{{a}}}
 because the {{{a}}} was in a denominator and
you must keep it in the denominator after canceling
out the {{{(b-1)}}}'s by putting a 1 over it.

Edwin</pre>