What is ((-x^2+4x-3))/((2x-8))>0 ?

The solution to ((-x^2+4x-3))/((2x-8))>0 is x<1\lor 3<x<4

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((-x^2+4x-3))/((2x-8))>0

\frac{( - x ^{2} + 4 x - 3 )}{( 2 x - 8 )} > 0

x < 1 or 3 < x < 4

Interval Notation

(- \infty, 1) \cup (3, 4)

Solution steps

\frac{- x ^{2} + 4 x - 3}{2 x - 8} > 0

Factor

\frac{- x ^{2} + 4 x - 3}{2 x - 8} : \frac{- ( x - 1 ) ( x - 3 )}{2 ( x - 4 )}

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

Simplify

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Multiply both sides by

2

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

Simplify

\frac{( x - 1 ) ( x - 3 )}{x - 4} < 0

Identify the intervals

x < 1 or 3 < x < 4

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

x^{2} \cdot (x + 2) < 0

\frac{( x - 12 ) ( x - 4 )}{( x ^{2} - 16 )} > 0

\frac{( 12 x )}{( x + 2 )} < 1

(x + 4) (x - 8) > 3 (x - 8)

What is ((-x^2+4x-3))/((2x-8))>0 ?
The solution to ((-x^2+4x-3))/((2x-8))>0 is x<1\lor 3<x<4