Factoring a repeated term reveals x = 1 as the sole solution to the quadratic equation.
Multiply both sides by x + 2:
(x² - 4x + 3) - (x + 2) = 0
Expand and simplify:
x² - 4x + 3 - x - 2 = 0
x² - 5x + 1 = 0
Factor the quadratic:
(x - 1)(x - 1) = 0
Solve for x:
x = 1
Therefore, the only solution to the equation is x = 1.
Note: Since the quadratic equation factors into the same term twice, there is only one distinct solution.
Complete question:
Solve the quadratic equation (x² - 4x + 3) / (x + 2) - 1 = 0 for x.