Question 195843

{{{((2x^2-x-3)/(x^2-1))((x^2+x-2)/(2x^2+x-6))}}} Start with the given expression.



{{{(((x+1)(2x-3))/(x^2-1))((x^2+x-2)/(2x^2+x-6))}}} Factor {{{2x^2-x-3}}} to get {{{(x+1)(2x-3)}}}.



{{{(((x+1)(2x-3))/((x-1)(x+1)))((x^2+x-2)/(2x^2+x-6))}}} Factor {{{x^2-1}}} to get {{{(x-1)(x+1)}}}.



{{{(((x+1)(2x-3))/((x-1)(x+1)))(((x+2)(x-1))/(2x^2+x-6))}}} Factor {{{x^2+x-2}}} to get {{{(x+2)(x-1)}}}.



{{{(((x+1)(2x-3))/((x-1)(x+1)))(((x+2)(x-1))/((x+2)(2x-3)))}}} Factor {{{2x^2+x-6}}} to get {{{(x+2)(2x-3)}}}.



{{{((x+1)(2x-3)(x+2)(x-1))/((x-1)(x+1)(x+2)(2x-3))}}} Combine the fractions. 



{{{(highlight((x+1))highlight((2x-3))highlight((x+2))highlight((x-1)))/(highlight((x-1))highlight((x+1))highlight((x+2))highlight((2x-3)))}}} Highlight the common terms. 



{{{(cross((x+1))cross((2x-3))cross((x+2))cross((x-1)))/(cross((x-1))cross((x+1))cross((x+2))cross((2x-3)))}}} Cancel out the common terms. 



{{{1}}} Simplify. 



So {{{((2x^2-x-3)/(x^2-1))((x^2+x-2)/(2x^2+x-6))}}} simplifies to {{{1}}}.



In other words, {{{((2x^2-x-3)/(x^2-1))((x^2+x-2)/(2x^2+x-6))=1}}} where {{{x<>-2}}}, {{{x<>-1}}}, {{{x<>1}}}, or {{{x<>3/2}}}