Final answer:
The expression (4x^2-4x)/(x^2-64) simplifies to (4x(x - 1))/(x + 8)(x - 8) after factoring both the numerator and the denominator, which cannot be simplified further.
Step-by-step explanation:
The expression given is (4x^2-4x)/(x^2-64). We can factor both the numerator and the denominator. The numerator can be factored by taking out a common factor of 4x, and the denominator is a difference of squares.
Let's factor the expression step by step:
- Factor the numerator: 4x(x - 1)
- Factor the denominator: (x + 8)(x - 8)
- The simplified expression: (4x(x - 1))/(x + 8)(x - 8)
- As there are no common factors in the numerator and the denominator that can be cancelled out, the expression is already in its simplest form.
Therefore, the simplified expression is: (4x(x - 1))/(x + 8)(x - 8)