Question 167741


{{{(3x^2-4x-15)/(x^2-4x+3)}}} Start with the given expression.



{{{((3x+5)(x-3))/(x^2-4x+3)}}} Factor {{{3x^2-4x-15}}} to get {{{(3x+5)(x-3)}}}.



{{{((3x+5)(x-3))/((x-1)(x-3))}}} Factor {{{x^2-4x+3}}} to get {{{(x-1)(x-3)}}}.



{{{((3x+5)highlight((x-3)))/((x-1)highlight((x-3)))}}} Highlight the common terms. 



{{{((3x+5)cross((x-3)))/((x-1)cross((x-3)))}}} Cancel out the common terms. 



{{{(3x+5)/(x-1)}}} Simplify. 



So {{{(3x^2-4x-15)/(x^2-4x+3)}}} simplifies to {{{(3x+5)/(x-1)}}}.



In other words, {{{(3x^2-4x-15)/(x^2-4x+3)=(3x+5)/(x-1)}}} where {{{x<>1}}} or {{{x<>3}}}