Question 178842


{{{((x^2-5x+4)/(x^2-1))((x^2+5x+4)/(x^2-9))}}} Start with the given expression.



{{{(((x-1)(x-4))/(x^2-1))((x^2+5x+4)/(x^2-9))}}} Factor {{{x^2-5x+4}}} to get {{{(x-1)(x-4)}}}.



{{{(((x-1)(x-4))/((x-1)(x+1)))((x^2+5x+4)/(x^2-9))}}} Factor {{{x^2-1}}} to get {{{(x-1)(x+1)}}}.



{{{(((x-1)(x-4))/((x-1)(x+1)))(((x+4)(x+1))/(x^2-9))}}} Factor {{{x^2+5x+4}}} to get {{{(x+4)(x+1)}}}.



{{{(((x-1)(x-4))/((x-1)(x+1)))(((x+4)(x+1))/((x-3)(x+3)))}}} Factor {{{x^2-9}}} to get {{{(x-3)(x+3)}}}.



{{{((x-1)(x-4)(x+4)(x+1))/((x-1)(x+1)(x-3)(x+3))}}} Combine the fractions. 



{{{(highlight((x-1))(x-4)(x+4)highlight((x+1)))/(highlight((x-1))highlight((x+1))(x-3)(x+3))}}} Highlight the common terms. 



{{{(cross((x-1))(x-4)(x+4)cross((x+1)))/(cross((x-1))cross((x+1))(x-3)(x+3))}}} Cancel out the common terms. 



{{{((x-4)(x+4))/((x-3)(x+3))}}} Simplify. 



{{{(x^2-16)/(x^2-9)}}} FOIL



So {{{((x^2-5x+4)/(x^2-1))((x^2+5x+4)/(x^2-9))}}} simplifies to {{{(x^2-16)/(x^2-9)}}}.



In other words, {{{((x^2-5x+4)/(x^2-1))((x^2+5x+4)/(x^2-9))=(x^2-16)/(x^2-9)}}} where {{{x<>-3}}}, {{{x<>-1}}}, {{{x<>1}}}, or {{{x<>3}}} (these are the restrictions)