What is ((-x^2+4x-3))/((2x-6))<0 ?

The solution to ((-x^2+4x-3))/((2x-6)) 1

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((-x^2+4x-3))/((2x-6))<0

\frac{( - x ^{2} + 4 x - 3 )}{( 2 x - 6 )} < 0

x > 1

Interval Notation

(1, \infty)

Solution steps

\frac{- x ^{2} + 4 x - 3}{2 x - 6} < 0

Factor

\frac{- x ^{2} + 4 x - 3}{2 x - 6} : \frac{- ( x - 1 ) ( x - 3 )}{2 ( x - 3 )}

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

Simplify

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

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

Multiply both sides by

2

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

Simplify

x - 1 > 0

Identify the intervals

x > 1

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

x^{4} + 6 x^{3} + 6 x^{2} + 6 x + 5 > 0

x \cdot (x - 1) \geq 0

(x^{2} - 9)^{2} \cdot (x + 1) (x^{2} - 2 x - 3) (x - 1) \geq 0

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

What is ((-x^2+4x-3))/((2x-6))<0 ?
The solution to ((-x^2+4x-3))/((2x-6))<0 is x>1