What is ((2x-1)(x-1)^2(x-2)^3)/((x-4)^4)>0 ?

The solution to ((2x-1)(x-1)^2(x-2)^3)/((x-4)^4)>0 is x 4

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((2x-1)(x-1)^2(x-2)^3)/((x-4)^4)>0

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

x < \frac{1}{2} or 2 < x < 4 or x > 4

Interval Notation

(- \infty, \frac{1}{2}) \cup (2, 4) \cup (4, \infty)

Decimal Notation

x < 0.5 or 2 < x < 4 or x > 4

Solution steps

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

Identify the intervals

x < \frac{1}{2} or 2 < x < 4 or x > 4

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

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

- x^{2} + 8 x - 7 > 0

x^{2} + 2 x + 5 > 0

\frac{lo g _{10} ( 1 )}{2 x} > 0

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