Question 133681

{{{f(x)=(x+5)/(x^2-4)}}} Start with the given function



{{{x^2-4=0}}} Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain.





{{{(x-2)(x+2)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)





Now set each factor equal to zero:


{{{x-2=0}}} or {{{x+2=0}}}


{{{x=2}}} or {{{x=-2}}}  Now solve for x in each case



So our solutions are {{{x=2}}} or {{{x=-2}}}




Since {{{x=-2}}} and {{{x=2}}} make the denominator equal to zero, this means we must exclude {{{x=-2}}} and {{{x=2}}} from our domain