what is the most simplified version of this? (x^2/x^2+2x+1)/(3x/x^2-1)
since x^2+2x+1 = (x+1)(x+1)
and x^2-1 = (x+1)(x-1)
what you have is
x^2/(x+1)^2 ÷ 3x/(x-1)(x+1)
= x^2/(x+1)^2 * (x-1)(x+1)/3x
= x(x-1) / 3(x+1)
and x^2-1 = (x+1)(x-1)
what you have is
x^2/(x+1)^2 ÷ 3x/(x-1)(x+1)
= x^2/(x+1)^2 * (x-1)(x+1)/3x
= x(x-1) / 3(x+1)