To solve the equation:
(x-1)² - 2/(x-1) = 0
First, let's simplify the equation:
(x² - 2x + 1) - 2/(x-1) = 0(x² - 2x + 1) - 2/(x-1)
To simplify further, let's find a common denominator for the fraction:
(x² - 2x + 1) - 2(x-1)/(x-1) = 0(x² - 2x + 1) - 2(x-1)/(x-1)
Now, simplify in the numerator:
(x² - 2x + 1) - 2x + 2 = 0x² - 4x + 3 = 0
Now, we have a quadratic equation that can be factored:
(x-3)(x-1) = 0
So, x = 3 or x = 1
Therefore, the solutions to the equation are x = 3 or x = 1.
To solve the equation:
(x-1)² - 2/(x-1) = 0
First, let's simplify the equation:
(x² - 2x + 1) - 2/(x-1) = 0
(x² - 2x + 1) - 2/(x-1)
To simplify further, let's find a common denominator for the fraction:
(x² - 2x + 1) - 2(x-1)/(x-1) = 0
(x² - 2x + 1) - 2(x-1)/(x-1)
Now, simplify in the numerator:
(x² - 2x + 1) - 2x + 2 = 0
x² - 4x + 3 = 0
Now, we have a quadratic equation that can be factored:
(x-3)(x-1) = 0
So, x = 3 or x = 1
Therefore, the solutions to the equation are x = 3 or x = 1.