Question

Divide the following and state the restrictions. (x²-x-20)/(x²-25)-:-(3x+12)/(x+5)

Answer 1

To divide the given expression, find a common denominator and follow the steps to simplify the expression. The restrictions on x are that it cannot be equal to 5 or -5.

Step-by-step explanation:

To divide the given expression, we need to find a common denominator. The denominators are (x²-25) and (x+5). The common denominator is (x²-25)(x+5).

1. For the first fraction, multiply both the numerator and denominator by (x+5) to get (x²-x-20)(x+5).
2. For the second fraction, multiply both the numerator and denominator by (x²-25) to get (3x+12)(x²-25).
3. Now, we can rewrite the division expression as [(x²-x-20)(x+5)] / [(x²-25)(3x+12)].
4. Next, factorize all the quadratic expressions.
5. Cancel out any common factors between the numerator and denominator.
6. Simplify the expression if possible.

The restrictions for this expression are any values of x that make the denominator zero. So, x cannot be equal to 5 or -5 as these values would make the denominators equal to zero.