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

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

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

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

x = - 1

Solution steps

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

Multiply by LCM

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

Solve

x (x - 3) (- x + 3) - 2 (- x + 3) = (x - 1) (x - 3) : x = - 1, x = 3

x = - 1, x = 3

Verify Solutions

Find undefined (singularity) points:

x = 3

Since the equation is undefined for:

3

x = - 1

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

y, x = \frac{y + 1}{y - 2}

\frac{2}{x} = \frac{4}{28}

\frac{- 2}{3 - 5 y} = \frac{y}{3 - 2 y}

- 4 x + \frac{36}{x} = 0

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