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

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

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

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

x = 1, x = - 1

Solution steps

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

Multiply by LCM

3 x = - (x - 2) - 2 x (x - 2)

Solve

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

x = 1, x = - 1

Verify Solutions

Find undefined (singularity) points:

x = 2, x = 0

Combine undefined points with solutions:

x = 1, x = - 1

\frac{1}{x - 1} - \frac{3}{x - 4} = 0

\frac{- 7}{x + 4} = \frac{3}{x - 5}

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

2 x - \frac{6}{x} = \frac{3 + x}{4} - 6

\frac{7}{6} = \frac{2}{k}