What is (x(3-4x)(x+1))/((2x-5))<0 ?

The solution to (x(3-4x)(x+1))/((2x-5)) 5/2

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(x(3-4x)(x+1))/((2x-5))<0

\frac{x ( 3 - 4 x ) ( x + 1 )}{( 2 x - 5 )} < 0

x < - 1 or 0 < x < \frac{3}{4} or x > \frac{5}{2}

Interval Notation

(- \infty, - 1) \cup (0, \frac{3}{4}) \cup (\frac{5}{2}, \infty)

Decimal Notation

x < - 1 or 0 < x < 0.75 or x > 2.5

Solution steps

\frac{x ( 3 - 4 x ) ( x + 1 )}{2 x - 5} < 0

Identify the intervals

x < - 1 or 0 < x < \frac{3}{4} or x > \frac{5}{2}

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

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

\frac{x + 1}{x} > 2

x (2 x + 3) > 3 x^{2} + 5

x^{4} + 5 < 0

What is (x(3-4x)(x+1))/((2x-5))<0 ?
The solution to (x(3-4x)(x+1))/((2x-5))<0 is x<-1\lor 0<x< 3/4 \lor x> 5/2