To solve for when the inequality

((x+3) / (x^2-2*x+1)) > 0

we first need to find the critical points where the expression is equal to zero and where it is undefined. The denominator cannot be zero, so we factor it to get:

x^2 - 2x + 1 = (x-1)^2

This means that x cannot equal 1.

Setting the numerator equal to zero:

x + 3 = 0
x = -3

So the critical points are x = -3 and x = 1. We need to test the intervals between these points to determine when the expression is positive.

Choosing x = -4:

(((-4)+3) / ((-4)^2-2*(-4)+1)) = (-1) / (16+8+1) = -1 / 25

This is negative, so the interval to the left of -3 does not satisfy the inequality.

Choosing x = 0:

((0+3) / (0^2-2*(0)+1)) = 3 / 1 = 3

This is positive, so the interval between -3 and 1 satisfies the inequality.

Choosing x = 2:

((2+3) / (2^2-2*(2)+1)) = 5 / 1 = 5

This is positive, so the interval to the right of 1 satisfies the inequality.

Therefore, the solution to the inequality is:

x < -3 or x > 1