To solve the equation, we first need to simplify it:
6x - x^2 - 6 - (-2x) - 3 / x - 1 = 16x - x^2 - 6 + 2x - 3 / x - 1 = 1-x^2 + 8x - 9 / x - 1 = 1
Now, multiply both sides by (x - 1) to clear the fraction:
(-x^2 + 8x - 9) = (x - 1)
Next, move all terms to one side of the equation:
-x^2 + 8x - 9 - x + 1 = 0-x^2 + 7x - 8 = 0
Now, we can factorize the quadratic equation:
(x - 8)(x + 1) = 0
From this, we find the values of x:
x = 8x = -1
Therefore, the solutions to the equation are x = 8 and x = -1.
To solve the equation, we first need to simplify it:
6x - x^2 - 6 - (-2x) - 3 / x - 1 = 1
6x - x^2 - 6 + 2x - 3 / x - 1 = 1
-x^2 + 8x - 9 / x - 1 = 1
Now, multiply both sides by (x - 1) to clear the fraction:
(-x^2 + 8x - 9) = (x - 1)
Next, move all terms to one side of the equation:
-x^2 + 8x - 9 - x + 1 = 0
-x^2 + 7x - 8 = 0
Now, we can factorize the quadratic equation:
(x - 8)(x + 1) = 0
From this, we find the values of x:
x = 8
x = -1
Therefore, the solutions to the equation are x = 8 and x = -1.