What is the answer to |(x^2-x-6)/(x-3)|=5x-1 ?

The answer to |(x^2-x-6)/(x-3)|=5x-1 is x= 3/4

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|(x^2-x-6)/(x-3)|=5x-1

\frac{x ^{2} - x - 6}{x - 3} = 5 x - 1

x = \frac{3}{4}

Decimal Notation

x = 0.75

Solution steps

\frac{x ^{2} - x - 6}{x - 3} = 5 x - 1

Simplify

\frac{x ^{2} - x - 6}{x - 3} : ∣ x + 2 ∣

∣ x + 2 ∣ = 5 x - 1

Solve

∣ x + 2 ∣ = 5 x - 1 : x = \frac{3}{4}

x = \frac{3}{4}

Verify Solutions

Find undefined (singularity) points:

x = 3

Combine undefined points with solutions:

x = \frac{3}{4}

\frac{1}{x} = \frac{1}{4} + \frac{1}{12}

\frac{2 x - 5}{5 + 2 x} = \frac{7}{4}

\frac{1}{x} = 0.8489

7 + \frac{2}{x - 8} = x

\frac{1}{( x - 2 ) ^{2}} - \frac{12}{x - 2} + 35 = 0

What is the answer to |(x^2-x-6)/(x-3)|=5x-1 ?
The answer to |(x^2-x-6)/(x-3)|=5x-1 is x= 3/4
Solve for x: |(x^2-x-6)/(x-3)|=5x-1
The solution is x= 3/4