Final answer:
The equation (x²-x-12)/(x-4)=7 does not have a solution when evaluated at x = 4 because it leads to division by zero.
Step-by-step explanation:
To solve the equation (x²-x-12)/(x-4)=7 where x equals 4, you first take note that directly substituting x = 4 into the equation yields a division by zero, which is undefined. Therefore, we must approach the problem differently. We can factor the quadratic expression in the numerator which gives us (x-4)(x+3). When we cancel out the (x-4) term from the numerator and the denominator, we are left with x + 3 = 7. Solving for x, we subtract 3 from both sides which results in x = 4. However, since we divided by (x-4), we must exclude x = 4 from the possible solutions, since that would lead to division by zero. So, this equation has no solution when we try to evaluate it at x = 4.