What is |(x^2-6x+7)/(x-1)|< 2/(x-1) ?

The solution to |(x^2-6x+7)/(x-1)|< 2/(x-1) is 1<x<3\lor 3<x<5

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|(x^2-6x+7)/(x-1)|< 2/(x-1)

\frac{x ^{2} - 6 x + 7}{x - 1} < \frac{2}{x - 1}

1 < x < 3 or 3 < x < 5

Interval Notation

(1, 3) \cup (3, 5)

Solution steps

\frac{x ^{2} - 6 x + 7}{x - 1} < \frac{2}{x - 1}

Find positive and negative intervals

x < 1, 1 \leq x \leq 3 - 2, 3 - 2 < x < 3 + 2, x \geq 3 + 2

Solve the inequality for each interval

No Solution or 1 < x \leq 3 - 2 or (3 - 2 < x < 3 or 3 < x < 3 + 2) or 3 + 2 \leq x < 5

Merge Overlapping Intervals

1 < x < 3 or 3 < x < 5

1 x + 16 = 36

8 x^{4} + x

x^{2} - 14 x = - 49

\frac{1}{4} (x + 3) = \frac{1}{3} (x - 2) + 1

6 (x - 5) = 12

What is |(x^2-6x+7)/(x-1)|< 2/(x-1) ?
The solution to |(x^2-6x+7)/(x-1)|< 2/(x-1) is 1<x<3\lor 3<x<5