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

The answer to x-2/(x-2)=x+1 is x=0

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

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

x = 0

Solution steps

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

Subtract

x

from both sides

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

Simplify

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

Multiply both sides by

x - 2

- 2 = x - 2

Add

2

to both sides

- 2 + 2 = x - 2 + 2

Simplify

0 = x

Switch sides

x = 0

Verify Solutions

Find undefined (singularity) points:

x = 2

Combine undefined points with solutions:

x = 0

1 - \frac{1}{x ^{2}}

x - \frac{7}{x - 3} = \frac{3 x}{x - 3}

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

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

\frac{x}{x + 1} + 6 = \frac{1}{x ^{2} + x}