What is the answer to |((2x))/((x-1))|+x=3 ?

The answer to |((2x))/((x-1))|+x=3 is x=3-sqrt(6)

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|((2x))/((x-1))|+x=3

\frac{( 2 x )}{( x - 1 )} + x = 3

x = 3 - 6

Decimal Notation

x = 0.55051 \dots

Solution steps

\frac{( 2 x )}{( x - 1 )} + x = 3

Simplify

\frac{2 x}{x - 1} : \frac{2 ∣ x ∣}{∣ x - 1 ∣}

\frac{2 ∣ x ∣}{∣ x - 1 ∣} + x = 3

Multiply both sides by

∣ x - 1 ∣

2 ∣ x ∣ + x ∣ x - 1 ∣ = 3 ∣ x - 1 ∣

Solve

2 ∣ x ∣ + x ∣ x - 1 ∣ = 3 ∣ x - 1 ∣ : x = 3 - 6

x = 3 - 6

Verify Solutions

Find undefined (singularity) points:

x = 1

Combine undefined points with solutions:

x = 3 - 6

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

\frac{1718 + 60 f}{33 + f} = 60.95

\frac{x ^{4} + 1}{( x ^{4} )} = 119

y, 7 x^{2} - \frac{x}{y} + \frac{81}{x} = 26 + 5 y

\frac{- 1}{2 - x} = \frac{1}{3}

What is the answer to |((2x))/((x-1))|+x=3 ?
The answer to |((2x))/((x-1))|+x=3 is x=3-sqrt(6)
Solve for x: |((2x))/((x-1))|+x=3
The solution is x=3-sqrt(6)