Which statement best reflects the solution(s) of the equation? 1/x+1/x−3=x−2/x−3 a. There is only one solution: x = 1. The solution x = 3 is an extraneous solution. b. There are two solutions: x = 1 and x = 3. c. There is only one solution: x = 3. The solution x = 1 is an extraneous solution. d. There is only one solution: x = 1. The solution x = 0 is an extraneous solution.

Answer: Option A) There is only one solution: x = 1. The solution x = 3 is an extraneous solution.                 Step-by-step explanation:We are given the following equation:[tex]\displaystyle\frac{1}{x} + \frac{1}{x-3} = \frac{x-2}{x-3}[/tex]Solving the given equation, we have:[tex]\displaystyle\frac{1}{x} + \frac{1}{x-3} = \frac{x-2}{x-3}\\\\\frac{2x-3}{x(x-3)}=\frac{x-2}{x-2}\\\\2x-3 = x^2 - 2x\\x^2 - 4x + 3 = 0\\x^2 - x-3x + 3 = 0\\x(x-1)-3(x-3) = 0\\(x-3)(x-1) = 0\\x =1, x=3[/tex]Extraneous solutions:An extraneous solution is not a root of the original equation because it was excluded from the domain of the original equation.We may arrive to this solution but cannot consider it as a solution because it is not valid.But x = 3 cannot be a solution to the given equation as when put in the given equation it gives denominator zero.Thus, x = 1 is the solution of the given equation and x = 3 is an extraneous solution.