What is (x^2+4x)/(2x-1)<(-4)/(2x-1) ?

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

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(x^2+4x)/(2x-1)<(-4)/(2x-1)

\frac{x ^{2} + 4 x}{2 x - 1} < \frac{- 4}{2 x - 1}

x < - 2 or - 2 < x < \frac{1}{2}

Solution steps

\frac{x ^{2} + 4 x}{2 x - 1} < \frac{- 4}{2 x - 1}

Rewrite in standard form

\frac{x ^{2} + 4 x + 4}{2 x - 1} < 0

Factor

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

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

Identify the intervals

x < - 2 or - 2 < x < \frac{1}{2}

\frac{- 1}{2} - 1

4 x = 5

x^{2} - 4 x

2 x^{2} + 1 x - 1

5 \cdot 15

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