Question

enter the correct answer in the box.
what is the quotient?
\\(\frac{x^2 - 10x + 25}{(x - 5)(x + 5)}\\)

Explanation:

Step1: Factor the numerator

The numerator \(x^2 - 10x + 25\) is a perfect square trinomial, which can be factored as \((x - 5)^2\) since \((a - b)^2 = a^2 - 2ab + b^2\) and here \(a = x\), \(b = 5\) (\(2ab = 10x\)). So the expression becomes \(\frac{(x - 5)^2}{(x - 5)(x + 5)}\).

Step2: Cancel common factors

We can cancel out the common factor \((x - 5)\) from the numerator and the denominator (assuming \(x
eq5\) to avoid division by zero). After canceling, we are left with \(\frac{x - 5}{x + 5}\).

Answer:

\(\frac{x - 5}{x + 5}\)