Question 112304
{{{(x^2+3x)/(x^2+7x+12)}}} Start with the given expression 



{{{(x(x+3))/(x^2+7x+12)}}} Factor {{{x^2+3x}}} to get {{{x(x+3)}}}  (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>)


{{{(x(x+3))/((x+4)(x+3))}}} Factor {{{x^2+7x+12}}} to get {{{(x+4)(x+3)}}}  



{{{(x*cross((x+3)))/((x+4)cross((x+3)))}}} Cancel like terms



{{{x/(x+4)}}} Simplify


Remember, when x=-4 or x=-3 (by solving {{{(x+4)(x+3)=0}}}) , the denominator is zero. So for these values, the fraction is not defined.


So {{{(x^2+3x)/(x^2+7x+12)}}} simplifies to {{{x/(x+4)}}} with these restrictions.