Question

type an integer or a simplified fraction. us simplify the rational expression. \\(\frac{5t - 25}{t^2 - 25}\\) = \\(\square\\) (use integers or fractions for any numbers in the

Explanation:

Step1: Factor numerator and denominator

Factor the numerator \(5t - 25\) by taking out the common factor 5: \(5t - 25 = 5(t - 5)\).
Factor the denominator \(t^2 - 25\) using the difference of squares formula \(a^2 - b^2=(a + b)(a - b)\), where \(a = t\) and \(b = 5\): \(t^2 - 25=(t + 5)(t - 5)\).
So the expression becomes \(\frac{5(t - 5)}{(t + 5)(t - 5)}\).

Step2: Cancel common factors

Cancel out the common factor \((t - 5)\) from the numerator and the denominator (assuming \(t
eq5\) to avoid division by zero).
This leaves \(\frac{5}{t + 5}\).

Answer:

\(\frac{5}{t + 5}\)