x^-2x-8/x+2
Factor numerator
(x+2) (x-4)
----------
x+2
simplify
x-4
To factor the numerator, we can use the factoring method. In this case, we have x^-2x-8. To factor this quadratic expression, we need to find two numbers that multiply to -8 and add up to -2.
Let's list the factors of -8: 1, -1, 2, -2, 4, -4, 8, -8.
Out of these factors, the pair that adds up to -2 is -4 and +2. Therefore, we can rewrite the numerator as:
(x + 2)(x - 4).
Now, let's simplify the expression by canceling out the common factors in the numerator and denominator.
(x - 4) is a common factor in both the numerator and denominator. So, we can cancel it out, as long as x + 2 is not equal to zero (because we cannot divide by zero).
Therefore, the simplified expression is:
(x - 4) / (x + 2).