What is (3x+2)/(x-1)>x ?

The solution to (3x+2)/(x-1)>x is x<2-sqrt(6)\lor 1<x<2+sqrt(6)

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(3x+2)/(x-1)>x

\frac{3 x + 2}{x - 1} > x

x < 2 - 6 or 1 < x < 2 + 6

Interval Notation

(- \infty, 2 - 6) \cup (1, 2 + 6)

Decimal Notation

x < - 0.44948 \dots or 1 < x < 4.44948 \dots

Solution steps

\frac{3 x + 2}{x - 1} > x

Rewrite in standard form

\frac{- x ^{2} + 4 x + 2}{x - 1} > 0

Factor

- x^{2} + 4 x + 2 : - (x - 2 - 6) (x - 2 + 6)

\frac{- ( x - 2 - 6 ) ( x - 2 + 6 )}{x - 1} > 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x - 2 - 6 ) ( x - 2 + 6 ) ) ( - 1 )}{x - 1} < 0 \cdot (- 1)

Simplify

\frac{( x - 2 - 6 ) ( x - 2 + 6 )}{x - 1} < 0

Identify the intervals

x < 2 - 6 or 1 < x < 2 + 6

3 m (3 m + 6) - 3 (m^{2} + 4 m + 1)

(5 x^{3} y^{- 5}) (4 x y^{3})

∣ - 4 g - 2 ∣ = 10

3 x^{2} + 18 = 0

3 x - 12 > 15

What is (3x+2)/(x-1)>x ?
The solution to (3x+2)/(x-1)>x is x<2-sqrt(6)\lor 1<x<2+sqrt(6)