What is 1/(((x-1)(3-x)))<= 1 ?

The solution to 1/(((x-1)(3-x))) 3

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1/(((x-1)(3-x)))<= 1

\frac{1}{( ( x - 1 ) ( 3 - x ) )} \leq 1

x < 1 or x = 2 or x > 3

Interval Notation

(- \infty, 1) \cup x = 2 \cup (3, \infty)

Solution steps

\frac{1}{( x - 1 ) ( 3 - x )} \leq 1

Rewrite in standard form

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

Factor

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

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

Identify the intervals

x < 1 or x = 2 or x > 3

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

\frac{( x - x ^{2} )}{( x ^{2} + 2 x )} \geq 0

\frac{3 x - 5}{4 + 1} > \frac{1}{2 x - 1}

(4 x - 6)^{2} \geq (6 x - 4)^{2}

7 x^{9} - 4 > 17

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