To simplify the given expression \(\frac{3}{(x-2)}\div\frac{(x-2)}{(x^2-4x+4)}\), we can follow these steps:
Step 1: Invert the second fraction and change the division to multiplication:
\(\frac{3}{(x-2)}\cdot\frac{(x^2-4x+4)}{(x-2)}\)
Step 2: Simplify the numerator and denominator separately:
Numerator: \(3\)
Denominator: \((x-2)\)
The simplest form of the expression is \(\frac{3}{(x-2)}\).
