Question 763252
{{{3*x/(x^2 + x - 2) + 2/(x^2 - 4*x + 3)}}}

=

{{{3*x / ((x + 2)*(x - 1)) + 2/((x - 3)*(x - 1))}}}

=

{{{(3*x*(x - 3) + 2*(x + 2))/((x + 2)*(x - 1)*(x - 3))}}} LCD is (x+2)(x-1)(x-3)

=

{{{(3*x^2 - 9*x + 2*x + 4)/((x + 2)*(x - 1)*(x - 3))}}} expanding numerator

=

{{{(3*x^2 - 7*x + 4) / ((x + 2)*(x - 1)*(x - 3))}}}

=

{{{((3*x - 4)*(x - 1)) / ((x + 2)*(x - 1)*(x - 3))}}} factorizing numerator

=

{{{((3*x - 4)*cross((x - 1))) / ((x + 2)*cross((x - 1))*(x - 3))}}}

= 

{{{(3*x - 4)/((x + 2)*(x - 3))}}}


:)