What is the answer to (x+3)^{-1}=x^{-1}+x ?

The answer to (x+3)^{-1}=x^{-1}+x is x\approx-3.27901…

Solve for x: (x+3)^{-1}=x^{-1}+x

The solution is x\approx-3.27901…

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(x + 3)^{- 1} = x^{- 1} + x

x \approx - 3.27901 \dots

Solution steps

(x + 3)^{- 1} = x^{- 1} + x

Refine

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

Multiply by LCM

x = x + 3 + x^{2} (x + 3)

Solve

x = x + 3 + x^{2} (x + 3) : x \approx - 3.27901 \dots

x \approx - 3.27901 \dots

Verify Solutions

Find undefined (singularity) points:

x = - 3, x = 0

Combine undefined points with solutions:

x \approx - 3.27901 \dots

\frac{1}{x} = 0.5

\frac{1}{x} = 0.7

\frac{1}{x} = 0.6

\frac{1}{x} = 0.8

\frac{2 x}{x - 1} - \frac{1}{x} = 5

What is the answer to (x+3)^{-1}=x^{-1}+x ?
The answer to (x+3)^{-1}=x^{-1}+x is x\approx-3.27901…
Solve for x: (x+3)^{-1}=x^{-1}+x
The solution is x\approx-3.27901…