find the quotient x^2-64/x+8

To find the quotient of the expression (x^2-64)/(x+8), we can start by factoring the numerator and the denominator if possible.

1. Factor the numerator:
The numerator, x^2 - 64, can be written as the difference of squares: (x - 8)(x + 8).

2. Write the factored numerator and the denominator as a multiplication:
Now, the expression can be rewritten as [(x - 8)(x + 8)]/(x + 8).

3. Cancel out the common factor:
Notice that (x + 8) appears both in the factored numerator and denominator. We can cancel it out.

[(x - 8)(x + 8)]/(x + 8) = (x - 8) * (cancel out (x + 8))/(cancel out (x + 8))

4. Simplify the expression:
After canceling out (x + 8), we are left with:

(x - 8)

So, the quotient of (x^2 - 64)/(x + 8) is x - 8.