What is ((x+2))/((x-1))<4 ?

The solution to ((x+2))/((x-1)) 2

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((x+2))/((x-1))<4

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

x < 1 or x > 2

Interval Notation

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

Solution steps

\frac{x + 2}{x - 1} < 4

Rewrite in standard form

\frac{- 3 x + 6}{x - 1} < 0

Factor

\frac{- 3 x + 6}{x - 1} : \frac{- 3 ( x - 2 )}{x - 1}

\frac{- 3 ( x - 2 )}{x - 1} < 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 3 ( x - 2 ) ) ( - 1 )}{x - 1} > 0 \cdot (- 1)

Simplify

\frac{3 ( x - 2 )}{x - 1} > 0

Divide both sides by

3

\frac{\frac{3 ( x - 2 )}{x - 1}}{3} > \frac{0}{3}

Simplify

\frac{x - 2}{x - 1} > 0

Identify the intervals

x < 1 or x > 2

\frac{( 7 - 2 k )}{( 4 ( - k ) )} \leq 1

\frac{( 2 ( x - 4 ) )}{( ( x - 1 ) ( x - 7 ) )} \leq \frac{1}{( x - 2 )}

(x - 1) (x - 2) \cdot (x - 3)^{2} > 0

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

(x - 1)^{2} (x + 1)^{3} (x - 4) \geq 0