x+1 : x - 2 + 1 : x+2 = 2x : x*x - 4

I’m not sure how the expression should be read because ":" for ratios can be used in a few ways. A couple of common interpretations are:

1. Proportion of two ratios: (x+1)/(x−1) = (x+2)/(2x)

• Solve by cross-multiplication: 2x(x+1) = (x−1)(x+2)
• This gives: 2x^2 + 2x = x^2 + x − 2 ⇒ x^2 + x + 2 = 0
• Discriminant: 1 − 8 = −7, so no real solutions. Complex solutions are x = (−1 ± i√7)/2.
• Domain restrictions: x ≠ 0, x ≠ 1, x ≠ −2 (to keep denominators nonzero).

2. A three-term ratio on the left equals a two-term ratio on the right (x+1) : (x−1) : (x+2) = (2x) : (x^2 − 4)

• There isn’t a standard, unambiguous way to solve such a “three-term ratio equals two-term ratio” without a precisely defined interpretation. If this was your intent, please clarify the exact meaning (e.g., should it mean (x+1)/(x−1) = (x+2)/(2x) or something else?).

If you can confirm which interpretation you meant (or provide the exact intended equation), I’ll solve it step by step.