What is the answer to 1-2/(x-1)= 2/(x^2-3x+2) ?

The answer to 1-2/(x-1)= 2/(x^2-3x+2) is x=4

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1-2/(x-1)= 2/(x^2-3x+2)

1 - \frac{2}{x - 1} = \frac{2}{x ^{2} - 3 x + 2}

x = 4

Solution steps

1 - \frac{2}{x - 1} = \frac{2}{x ^{2} - 3 x + 2}

Multiply by LCM

(x - 1) (x - 2) - 2 (x - 2) = 2

Solve

(x - 1) (x - 2) - 2 (x - 2) = 2 : x = 4, x = 1

x = 4, x = 1

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 2

Since the equation is undefined for:

1

x = 4

4 + \frac{1}{x} - \frac{1}{x ^{2}} = 0

- 2 + \frac{x}{x + 2} = - \frac{7}{x + 2}

6 + \frac{x}{x + 1} = - \frac{1}{x + 1}

\frac{3}{x - 1} = \frac{4}{2 x + 3}

\frac{4 x}{3 x - 12} = \frac{1}{x - 4}

What is the answer to 1-2/(x-1)= 2/(x^2-3x+2) ?
The answer to 1-2/(x-1)= 2/(x^2-3x+2) is x=4
Solve for x: 1-2/(x-1)= 2/(x^2-3x+2)
The solution is x=4