(b-3)/(b^2-3b-4)

To simplify the expression \((b - 3)/(b^2 - 3b - 4)\), we first need to factor the denominator \(b^2 - 3b - 4\).

Step 1: Factor the Denominator

The expression \(b^2 - 3b - 4\) can be factored by looking for two numbers that multiply to \(-4\) (the constant term) and add to \(-3\) (the coefficient of \(b\)). These numbers are \(-4\) and \(1\).

Thus, we can factor the denominator as follows: \[ b^2 - 3b - 4 = (b - 4)(b + 1) \]

Step 2: Rewrite the Expression

Now, we can rewrite the original expression with the factored form of the denominator: \[ \frac{b - 3}{b^2 - 3b - 4} = \frac{b - 3}{(b - 4)(b + 1)} \]

Step 3: Conclusion

Since there are no common factors in the numerator and the denominator, the expression is in its simplest form. Therefore, the simplified expression is: \[ \frac{b - 3}{(b - 4)(b + 1)} \]

Final Result

\[ \frac{b - 3}{(b - 4)(b + 1)} \]