Question

simplify.
\\(\dfrac{\dfrac{u - 2}{u}}{\dfrac{u^2 - 4}{5u}}\\)

Explanation:

Step1: Rewrite division as multiplication

Dividing by a fraction is multiplying by its reciprocal, so \(\frac{\frac{u - 2}{u}}{\frac{u^2 - 4}{5u}}=\frac{u - 2}{u}\times\frac{5u}{u^2 - 4}\)

Step2: Factor the difference of squares

Factor \(u^2 - 4\) as \((u - 2)(u + 2)\), so the expression becomes \(\frac{u - 2}{u}\times\frac{5u}{(u - 2)(u + 2)}\)

Step3: Cancel common factors

Cancel \(u - 2\) and \(u\) (assuming \(u
eq0,2,-2\)), we get \(\frac{5}{u + 2}\)

Answer:

\(\dfrac{5}{u + 2}\)