Answer:
To solve the equation algebraically, we will follow these steps:
Step 1: Multiply both sides of the equation by x to eliminate the fraction:
12/x * x = (x - 1) * x
12 = x^2 - x
Step 2: Rearrange the equation to bring all terms to one side:
x^2 - x - 12 = 0
Step 3: Factor the quadratic equation:
(x - 4)(x + 3) = 0
Step 4: Set each factor equal to zero and solve for x:
x - 4 = 0 or x + 3 = 0
Step 5: Solve for x in each equation:
x = 4 or x = -3
Therefore, the solutions to the equation 12/x = x - 1 are x = 4 and x = -3.
Step-by-step explanation:
