Final answer:
To simplify the rational expression, factor the numerators and denominators, cancel out common factors, and simplify the expression to (x + 4)/(x + 5). There are no restrictions on the variable.
Step-by-step explanation:
To simplify the rational expression (x²-11x+30)/(x²-25)*(x²+9x+20)/(x²-2x-24), we can factor the numerators and denominators.
First, factor each quadratic expression:
- x² - 11x + 30 = (x - 5)(x - 6)
- x² + 9x + 20 = (x + 4)(x + 5)
- x² - 25 = (x - 5)(x + 5)
- x² - 2x - 24 = (x - 6)(x + 4)
Now, we can cancel out common factors in the numerators and denominators:
(x - 5)(x - 6)/(x - 5)(x + 5) * (x + 4)(x + 5)/(x - 6)(x + 4)
After canceling out the common factors, we are left with:
(x + 4)/(x + 5)
There are no restrictions on the variable since we did not encounter any division by zero or undefined values in the original expression.
Learn more about Simplifying rational expressions