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

Answer

Expert–verified

Hide Steps

Answer

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

Steps

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 $\boxed{\frac{x-1}{x-5}}$