Answer:
x = 2
Step-by-step explanation:
To begin x ≠ 0 , x ≠ 1 as this would make the denominators zero , making them undefined.
[tex]\frac{x}{x-1}[/tex] = [tex]\frac{1}{x-1}[/tex] + [tex]\frac{2}{x}[/tex]
Multiply through by x(x - 1), the LCM of x and x - 1 , to clear the fractions
x² = x + 2(x - 1)
x² = x + 2x - 2
x² = 3x - 2 ( subtract 3x - 2 from both sides )
x² - 3x + 2 = 0 ← in standard form
(x - 1)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 2 = 0 ⇒ x = 2
Since x ≠ 1 then solution is x = 2
