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

The answer to e(x)= 1/x-1/(|x|) is x=-sqrt(2/e)

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e(x)= 1/x-1/(|x|)

e (x) = \frac{1}{x} - \frac{1}{∣ x ∣}

x = - \frac{2}{e}

Decimal Notation

x = - 0.85776 \dots

Solution steps

e (x) = \frac{1}{x} - \frac{1}{∣ x ∣}

Multiply by LCM

e x^{2} ∣ x ∣ = ∣ x ∣ - x

Solve

e x^{2} ∣ x ∣ = ∣ x ∣ - x : x = - \frac{2}{e} or x = 0

x = - \frac{2}{e}, x = 0

Verify Solutions

Find undefined (singularity) points:

x = 0

Since the equation is undefined for:

0

x = - \frac{2}{e}

\frac{( ( 1 - x ) ^{3} ( x + 2 ) ^{4} )}{( ( x + 9 ) ^{2} ( x - 8 ) )} = 0

9.6 = \frac{- 1}{10 ( x - 12 ) ^{2} + 10}

2 (\frac{x - 1}{x})^{2} - 5 (\frac{x + 1}{x + 2}) + 18 = 0

\frac{( x ^{- 2} )}{x} = \frac{1}{( x ^{12} )}

\frac{( x - 6 )}{( x + 4 )} = 0

What is the answer to e(x)= 1/x-1/(|x|) ?
The answer to e(x)= 1/x-1/(|x|) is x=-sqrt(2/e)