x²-6/x-3=x/x-3

Assuming the equation is (x^2 − 6)/(x − 3) = x/(x − 3).

Steps:

• Domain: x ≠ 3 (denominators must not be zero).
• Subtract the right side: (x^2 − 6)/(x − 3) − x/(x − 3) = 0 ⇒ (x^2 − 6 − x)/(x − 3) = 0 ⇒ x^2 − x − 6 = 0 (since x ≠ 3).
• Factor: (x − 3)(x + 2) = 0 ⇒ x = 3 or x = −2.
• Exclude x = 3 due to the domain restriction; thus x = −2.

Answer: x = −2. (If you meant a different interpretation of the expression, please clarify.)