Like when adding/subtracting fractions at any other time, you need a common denominator, in this case (x-1)(x+1)=x^2-1 so:
(2(x+1)+3(x-1))/(x^2-1)=4 multiply both sides by (x^2-1)
2x+2+3x-3=4x^2-4 combine like terms on left
5x-1=4x^2-4 subtract (5x-1) from both sides
4x^2-5x-3=0 using the quadratic formula for expediency
x=(5±√73)/8
x≈-0.443 and 1.693
