Questions: Perform the multiplication or division and simplify. (x^2+4x-5)/(x^2-25) * (x-5)/(x+4)

Solution Steps

To simplify the given expression, we need to factorize the polynomials in the numerators and denominators, cancel out common factors, and then perform the multiplication.

1. Factorize \(x^2 + 4x - 5\) and \(x^2 - 25\).
2. Simplify the expression by canceling out common factors.
3. Multiply the remaining fractions.

We start by factorizing the polynomials in the numerators and denominators.

\[ x^2 + 4x - 5 = (x - 1)(x + 5) \] \[ x^2 - 25 = (x - 5)(x + 5) \]

Substitute the factored forms into the original expression:

\[ \frac{(x - 1)(x + 5)}{(x - 5)(x + 5)} \cdot \frac{x - 5}{x + 4} \]

Cancel the common factors \((x + 5)\) and \((x - 5)\) from the numerator and the denominator:

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

Final Answer