Zachrteyeetidn
Answered

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

Sagot :

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

Rspill6idn

Answer:  -0.5615 and 3.5615

Step-by-step explanation:

x/(x-1) = 1/(x-1) + 2/x

x = 1 +2*(x-1)/x :  Multiply both sides by (x-1)

x^2 = x + 2x + 2  :  Multiply both sides by x

x^2 -3x -2 = 0  :  Rearrange to form a quadratice equation

Solve using the quadritic equation or by graphing and finding the x intercepts.  It has two intercepts, at -0.56155 and 3.56155.

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