Question 153225


{{{(r^2-5r+6)/(r^2-4)}}} Start with the given expression.



{{{((r-2)(r-3))/(r^2-4)}}} Factor {{{r^2-5r+6}}} to get {{{(r-2)(r-3)}}}.



{{{((r-2)(r-3))/((r-2)(r+2))}}} Factor {{{r^2-4}}} to get {{{(r-2)(r+2)}}}.



{{{(highlight((r-2))(r-3))/(highlight((r-2))(r+2))}}} Highlight the common terms. 



{{{(cross((r-2))(r-3))/(cross((r-2))(r+2))}}} Cancel out the common terms. 



{{{(r-3)/(r+2)}}} Simplify. 



So {{{(r^2-5r+6)/(r^2-4)}}} simplifies to {{{(r-3)/(r+2)}}}.



In other words, {{{(r^2-5r+6)/(r^2-4)=(r-3)/(r+2)}}} where {{{r<>-2}}} or {{{r<>2}}}