What is the answer to (x-2)^{-1}=x^{-1}+x ?

The answer to (x-2)^{-1}=x^{-1}+x is x\approx 2.35930…

Solve for x: (x-2)^{-1}=x^{-1}+x

The solution is x\approx 2.35930…

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(x - 2)^{- 1} = x^{- 1} + x

x \approx 2.35930 \dots

Solution steps

(x - 2)^{- 1} = x^{- 1} + x

Refine

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

Multiply by LCM

x = x - 2 + x^{2} (x - 2)

Solve

x = x - 2 + x^{2} (x - 2) : x \approx 2.35930 \dots

x \approx 2.35930 \dots

Verify Solutions

Find undefined (singularity) points:

x = 2, x = 0

Combine undefined points with solutions:

x \approx 2.35930 \dots

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

\frac{1}{x} + x = 5

\frac{3}{x} = x

x, y = \frac{x}{x + 2}

(2 + j^{3}) = \frac{s + 1}{s - 2}

What is the answer to (x-2)^{-1}=x^{-1}+x ?
The answer to (x-2)^{-1}=x^{-1}+x is x\approx 2.35930…
Solve for x: (x-2)^{-1}=x^{-1}+x
The solution is x\approx 2.35930…