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

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

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

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

x < 0 or \frac{1}{4} < x < 1

Interval Notation

(- \infty, 0) \cup (\frac{1}{4}, 1)

Decimal Notation

x < 0 or 0.25 < x < 1

Solution steps

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

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

x < 0 or \frac{1}{4} < x < 1

x^{3} - 4 x^{2} + 3 x < 0

36 m^{2} - 180 m + 144 < 0

\frac{x}{( x - 6 )} \geq 0

\frac{4}{( x - 5 )} - \frac{2}{( x - 5 )} > \frac{( 3 x + 3 )}{( x ^{2} - 25 )}

- 4 - 3 x^{2} > 0

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