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

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

Solve for x: 1/(x-1)=x+1

The solution is x=sqrt(2),x=-sqrt(2)

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

x = 2, x = - 2

Decimal Notation

x = 1.41421 \dots, x = - 1.41421 \dots

Solution steps

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

Multiply both sides by

x - 1

1 = x (x - 1) + x - 1

Solve

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

x = 2, x = - 2

Verify Solutions

Find undefined (singularity) points:

x = 1

Combine undefined points with solutions:

x = 2, x = - 2

\frac{x - 6}{x - 2} = - \frac{9}{x}

\frac{8}{3 x} = 1

\frac{3}{x - 1} - \frac{8}{x + 2} = 1

\frac{8}{x + 2} - 4 = 10

28 + x = \frac{5}{9 ( 60 + x )}

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