What is the answer to (x+6)^{-1}=x^{-1}+x ?

The answer to (x+6)^{-1}=x^{-1}+x is x\approx-6.15821…

Solve for x: (x+6)^{-1}=x^{-1}+x

The solution is x\approx-6.15821…

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(x + 6)^{- 1} = x^{- 1} + x

x \approx - 6.15821 \dots

Solution steps

(x + 6)^{- 1} = x^{- 1} + x

Refine

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

Multiply by LCM

x = x + 6 + x^{2} (x + 6)

Solve

x = x + 6 + x^{2} (x + 6) : x \approx - 6.15821 \dots

x \approx - 6.15821 \dots

Verify Solutions

Find undefined (singularity) points:

x = - 6, x = 0

Combine undefined points with solutions:

x \approx - 6.15821 \dots

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

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

a, g = b - \frac{c}{a}

4 = (\frac{1}{( 2 + x )}) + 1

F = \frac{G m _{1} m _{2}}{d ^{2}}

What is the answer to (x+6)^{-1}=x^{-1}+x ?
The answer to (x+6)^{-1}=x^{-1}+x is x\approx-6.15821…
Solve for x: (x+6)^{-1}=x^{-1}+x
The solution is x\approx-6.15821…