Final answer:
Use the quadratic formula to find the solutions for x, which are x = 4 and x = -2.
Step-by-step explanation:
To solve the equation (x²-2x−8)/( x -6)= 0, we can start by multiplying both sides of the equation by (x - 6) to eliminate the denominator. This gives us x² - 2x - 8 = 0. Now, we can use the quadratic formula to find the solutions for x.
The quadratic formula is x = (-b ± √(b² - 4ac))/(2a), where a = 1, b = -2, and c = -8 in this case.
Plugging in these values, we get x = (2 ± √((-2)² - 4(1)(-8)))/(2(1)).
Simplifying further, we have x = (2 ± √(4 + 32))/2, which simplifies to x = (2 ± √(36))/2.
Therefore, the two solutions for x are x = (2 + 6)/2 = 4 and x = (2 - 6)/2 = -2.