Question

1. \\(\frac{m - 3}{m^2 - 2m - 3}\\)

Explanation:

Step1: Factor the denominator

We factor the quadratic expression in the denominator \(m^2 - 2m - 3\). We need two numbers that multiply to \(-3\) and add to \(-2\). The numbers are \(-3\) and \(1\), so \(m^2 - 2m - 3=(m - 3)(m+ 1)\).

Step2: Simplify the fraction

Now we have the fraction \(\frac{m - 3}{(m - 3)(m + 1)}\). Assuming \(m
eq3\) (to avoid division by zero), we can cancel out the common factor \((m - 3)\) from the numerator and the denominator. So the simplified form is \(\frac{1}{m + 1}\) (for \(m
eq3\) and \(m
eq - 1\)).

Answer:

\(\frac{1}{m + 1}\) (with the restrictions \(m
eq3\) and \(m
eq - 1\))