Divide. (x^2-4/x-8)/x-2
A. (x-2)(x+2)/x-8
B. x-8/x+2
C. x-2/x-8
D. x+2/x-8
AAAaannndd the bot gets it wrong yet again!
[(x^2-4)/(x-8)]/(x-2) = (x-2)(x+2)/(x-8)/(x-2) = (x+2)/(x-8)
I apologize for the mistake in my previous response. You are correct that the simplified form of [(x^2-4)/(x-8)]/(x-2) is (x+2)/(x-8). Thank you for correcting me.
To divide the expression (x^2 - 4)/(x - 8) by (x - 2), you need to perform polynomial division. Here's how you can do it step-by-step:
Step 1: Factor the numerator, if possible.
The numerator (x^2 - 4) is a difference of squares, which can be factored as (x - 2)(x + 2).
Step 2: Rewrite the division problem.
Now, the expression becomes [(x - 2)(x + 2)/(x - 8)] ÷ (x - 2).
Step 3: Cancel out common factors.
You can cancel out the factor (x - 2) in both the numerator and denominator.
Step 4: Simplify the expression.
After canceling out (x - 2), the expression simplifies to (x + 2)/(x - 8).
Therefore, the correct answer is option D: (x + 2)/(x - 8).
To divide fractions, we need to multiply by the reciprocal of the second fraction. Therefore:
[x^2-4/x-8]/(x-2) = (x^2-4/x-8) * (1/(x-2))
Next, we can factor the numerator of the first fraction as the difference of squares:
[(x+2)(x-2)/x-8] * (1/(x-2))
We can then cancel the x-2 in the numerator and denominator:
(x+2)/(x-8)
Therefore, the answer is A. (x-2)(x+2)/x-8.