Simplify the given expression: $\frac{x^{2}+3 x-4}{x^{2}-x-20}=$

Step 1 ：Given the expression \(\frac{x^{2}+3 x-4}{x^{2}-x-20}\)

Step 2 ：To simplify it, we can factorize the numerator and the denominator.

Step 3 ：The factorized form of the numerator \(x^{2}+3 x-4\) is \((x - 1)(x + 4)\)

Step 4 ：The factorized form of the denominator \(x^{2}-x-20\) is \((x - 5)(x + 4)\)

Step 5 ：After factorizing, we can cancel out the common factors from the numerator and the denominator, which is \((x + 4)\)

Step 6 ：So, the simplified expression is \(\frac{x - 1}{x - 5}\)

Step 7 ：Final Answer: The simplified form of the given expression is \(\boxed{\frac{x-1}{x-5}}\)