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

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

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

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

x = 3, x = 1

Solution steps

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

Move

3

to the right side

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

Multiply both sides by

x - 2

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

Solve

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

x = 3, x = 1

Verify Solutions

Find undefined (singularity) points:

x = 2

Combine undefined points with solutions:

x = 3, x = 1

2 + \frac{3}{x} = \frac{11}{4}

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

\frac{5}{x + 3} + \frac{4}{x + 2} = 2

28 a^{- 2} + 45 a^{- 1} - 7 = 0

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