What is ((x^2-5x+6))/((x-1))>0 ?

The solution to ((x^2-5x+6))/((x-1))>0 is 1 3

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((x^2-5x+6))/((x-1))>0

\frac{( x ^{2} - 5 x + 6 )}{( x - 1 )} > 0

1 < x < 2 or x > 3

Interval Notation

(1, 2) \cup (3, \infty)

Solution steps

\frac{x ^{2} - 5 x + 6}{x - 1} > 0

Factor

\frac{x ^{2} - 5 x + 6}{x - 1} : \frac{( x - 2 ) ( x - 3 )}{x - 1}

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

Identify the intervals

1 < x < 2 or x > 3

\frac{( ( x - 3 ) ^{2} )}{( ( x + 5 ) ( 1 - x ) )} \geq 0

\frac{3}{x - 2} > 4

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

\frac{5}{( x - 2 )} > 0

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

What is ((x^2-5x+6))/((x-1))>0 ?
The solution to ((x^2-5x+6))/((x-1))>0 is 1<x<2\lor x>3