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

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

Solve for x: 1/(x-2)= 1/x+2

The solution is x=1+sqrt(2),x=1-sqrt(2)

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

x = 1 + 2, x = 1 - 2

Decimal Notation

x = 2.41421 \dots, x = - 0.41421 \dots

Solution steps

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

Multiply by LCM

x = x - 2 + 2 x (x - 2)

Solve

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

x = 1 + 2, x = 1 - 2

Verify Solutions

Find undefined (singularity) points:

x = 2, x = 0

Combine undefined points with solutions:

x = 1 + 2, x = 1 - 2

\frac{x ^{2} - 25}{x + 5} + 5 x = 0

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

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

0.078 = \frac{0.2 + x}{2 - 2 x}

\frac{- 2 x ^{2} + a x - 35}{3 x + 15}

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