What is the answer to |(x^2)/(x-1)|=4 ?

The answer to |(x^2)/(x-1)|=4 is x=-2(1+sqrt(2)),x=2(sqrt(2)-1),x=2

Solve for x: |(x^2)/(x-1)|=4

The solution is x=-2(1+sqrt(2)),x=2(sqrt(2)-1),x=2

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\frac{x ^{2}}{x - 1} = 4

x = - 2 (1 + 2), x = 2 (2 - 1), x = 2

Decimal Notation

x = - 4.82842 \dots, x = 0.82842 \dots, x = 2

Solution steps

\frac{x ^{2}}{x - 1} = 4

Simplify

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

\frac{∣ x ∣ ^{2}}{∣ x - 1 ∣} = 4

Multiply both sides by

∣ x - 1 ∣

∣ x ∣^{2} = 4 ∣ x - 1 ∣

Solve

∣ x ∣^{2} = 4 ∣ x - 1 ∣ : x = - 2 (1 + 2) or x = 2 (2 - 1) or x = 2

x = - 2 (1 + 2), x = 2 (2 - 1), x = 2

Verify Solutions

Find undefined (singularity) points:

x = 1

Combine undefined points with solutions:

x = - 2 (1 + 2), x = 2 (2 - 1), x = 2

t^{- 2} - 7 t^{- 1} + 12 = 0

0 = 1 + \frac{1}{x ^{2}}

y, \frac{1}{x} + \frac{1}{y} = \frac{1}{2023}

x + \frac{6}{x} = - 5

\frac{1}{x - 1} + 4 = \frac{1}{x ^{2} - x}

What is the answer to |(x^2)/(x-1)|=4 ?
The answer to |(x^2)/(x-1)|=4 is x=-2(1+sqrt(2)),x=2(sqrt(2)-1),x=2
Solve for x: |(x^2)/(x-1)|=4
The solution is x=-2(1+sqrt(2)),x=2(sqrt(2)-1),x=2