What is (x-2)/(x^2-5x+6)<= 1 ?

The solution to (x-2)/(x^2-5x+6) = 4

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(x-2)/(x^2-5x+6)<= 1

\frac{x - 2}{x ^{2} - 5 x + 6} \leq 1

x < 3 or x \geq 4

Interval Notation

(- \infty, 3) \cup [4, \infty)

Solution steps

\frac{x - 2}{x ^{2} - 5 x + 6} \leq 1

Rewrite in standard form

\frac{- x ^{2} + 6 x - 8}{x ^{2} - 5 x + 6} \leq 0

Factor

\frac{- x ^{2} + 6 x - 8}{x ^{2} - 5 x + 6} : \frac{- ( x - 2 ) ( x - 4 )}{( x - 2 ) ( x - 3 )}

\frac{- ( x - 2 ) ( x - 4 )}{( x - 2 ) ( x - 3 )} \leq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x - 2 ) ( x - 4 ) ) ( - 1 )}{( x - 2 ) ( x - 3 )} \geq 0 \cdot (- 1)

Simplify

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

\frac{x - 4}{x - 3} \geq 0

Identify the intervals

x < 3 or x \geq 4

- \frac{1}{3} x - 2 = \frac{2}{3} x - 2

- 84 = \frac{d}{3}

21 k^{3} - 84 k^{2} + 15 k - 60

x < 2 or x > - 2

2 x^{2} - 18 x = 0

What is (x-2)/(x^2-5x+6)<= 1 ?
The solution to (x-2)/(x^2-5x+6)<= 1 is x<3\lor x>= 4