Question 132142


{{{(r^3-7r)/(r^2-49)}}} Start with the given expression



{{{r^2-49=0}}} Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of r that make the denominator zero, then we must exclude them from the domain.





{{{(r-7)(r+7)=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:


{{{r-7=0}}} or {{{r+7=0}}}


{{{r=7}}} or {{{r=-7}}}  Now solve for r in each case



So our solutions are {{{r=7}}} or {{{r=-7}}}




Since {{{r=-7}}} and {{{r=7}}} make the denominator equal to zero, this means  {{{r=-7}}} and {{{r=7}}} make the rational expression undefined (remember you cannot divide by zero)