Answer:
The solutions to the equation 9 + 6/x = x + 10 are x = -3 and x = 2.
Explanation:
To solve the equation 9 + 6/x = x + 10 for x, we can follow these steps:
Subtract 9 from both sides of the equation to isolate the 6/x term:
6/x = x + 1
Multiply both sides of the equation by x to eliminate the fraction:
6 = x^2 + x
Rearrange the equation into standard quadratic form:
x^2 + x - 6 = 0
Factor the quadratic:
(x + 3)(x - 2) = 0
Use the zero product property to find the solutions:
x + 3 = 0 or x - 2 = 0
x = -3 or x = 2
Therefore, the solutions to the equation 9 + 6/x = x + 10 are x = -3 and x = 2.