How would i solve x/(x-1) = 1/(x-1) + 2/x

x = 2

Step-by-step explanation:

To begin x ≠ 0 , x ≠ 1 as this would make the denominators zero , making them undefined.

= +

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

step-by-step explanation:

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