Question 199580


{{{(b^2-9)/(b^3-27)}}} Start with the given expression.



{{{((b-3)*(b+3))/(b^3-27)}}} Factor {{{b^2-9}}} to get {{{(b-3)(b+3)}}} (use the difference of squares formula)



{{{((b-3)*(b+3))/((b-3)*(b^2+3*b+9))}}} Factor {{{b^3-27}}} to get {{{(b-3)(b^2+3b+9)}}} (use the difference of cubes formula)



{{{(highlight((b-3))(b+3))/(highlight((b-3))(b^2+3b+9))}}} Highlight the common terms. 



{{{(cross((b-3))(b+3))/(cross((b-3))(b^2+3b+9))}}} Cancel out the common terms. 



{{{(b+3)/(b^2+3b+9)}}} Simplify. 



So {{{(b^2-9)/(b^3-27)}}} simplifies to {{{(b+3)/(b^2+3b+9)}}}.



In other words, {{{(b^2-9)/(b^3-27)=(b+3)/(b^2+3b+9)}}} where {{{b<>3}}}