Questions: Solve the equation. 12/(n^2-2 n)+3=6/(n-2) The solution set is 1.

Solve the equation \( \frac{12}{n^{2}-2n}+3=\frac{6}{n-2} \).

Factor the denominator.

The denominator \( n^{2}-2n \) can be factored as \( n(n-2) \). Thus, the equation can be rewritten as: \[ \frac{12}{n(n-2)} + 3 = \frac{6}{n-2} \]

Rewrite the equation with a common denominator.

The equation becomes: \[ \frac{12 + 3(n(n-2))}{n(n-2)} = \frac{6}{n-2} \] This simplifies to: \[ 12 + 3(n^2 - 2n) = 6n \]

Simplify and solve the resulting quadratic equation.

Rearranging gives: \[ 3n^2 - 12n + 12 = 0 \] Factoring or using the quadratic formula, we find: \[ n = 2 \]

The solution to the equation is \( \boxed{n = 2} \).

The solution to the equation \( \frac{12}{n^{2}-2n}+3=\frac{6}{n-2} \) is \( \boxed{n = 2} \).