Question 549306
{{{f(x)=x/(x^2+2x-3)}}}




Note that the numerator can be any value of x.... but whenever we are dealing with fractions, the denominator cannot be 0 (check out any number divided by 0 on your calculator if you do not believe me.... you will end up getting an error)

This means that 
{{{x^2+2x-3}}} cannot be 0 

Well when does {{{x^2+2x-3=0}}}??
{{{x^2+2x-3}}}
Since our a value is 1, we need two values that multiply to our c value (-3) and add to our b value (2).   If you think about it you will see that 3 and -1 do the trick. 

So 
{{{x^2+2x-3=(x+3)(x-1)}}} 
and 
{{{(x+3)(x-1)=0}}} when x=-3 and x=1 

This means x can be anything except -3 and 1.  


Let me know if any of the steps I took you are not sure about:)   Merry Christmas!