What is the answer to |(x+1)/(x-5)|=1 ?

The answer to |(x+1)/(x-5)|=1 is x=2

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|(x+1)/(x-5)|=1

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

x = 2

Solution steps

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

Simplify

\frac{x + 1}{x - 5} : \frac{∣ x + 1 ∣}{∣ x - 5 ∣}

\frac{∣ x + 1 ∣}{∣ x - 5 ∣} = 1

Multiply both sides by

∣ x - 5 ∣

∣ x + 1 ∣ = ∣ x - 5 ∣

Solve

∣ x + 1 ∣ = ∣ x - 5 ∣ : x = 2

x = 2

Verify Solutions

Find undefined (singularity) points:

x = 5

Combine undefined points with solutions:

x = 2

1 - w \geq - 1

4 - 3 x - x^{2} = 2 x + 8

7^{2} + 3^{2} = c^{2}

∣ 3 x - 1 ∣ = 8

(x + 5)^{2} + 4 = 68