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

The solution to (x+2)/(x-1)<(2x)/(2x+3) is x<-3/2 \lor-2/3 <x<1

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(x+2)/(x-1)<(2x)/(2x+3)

\frac{x + 2}{x - 1} < \frac{2 x}{2 x + 3}

x < - \frac{3}{2} or - \frac{2}{3} < x < 1

Interval Notation

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

Decimal Notation

x < - 1.5 or - 0.66666 \dots < x < 1

Solution steps

\frac{x + 2}{x - 1} < \frac{2 x}{2 x + 3}

Rewrite in standard form

\frac{9 x + 6}{( x - 1 ) ( 2 x + 3 )} < 0

Factor

\frac{9 x + 6}{( x - 1 ) ( 2 x + 3 )} : \frac{3 ( 3 x + 2 )}{( x - 1 ) ( 2 x + 3 )}

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

Divide both sides by

3

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

Simplify

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

Identify the intervals

x < - \frac{3}{2} or - \frac{2}{3} < x < 1

x^{2} + 3 x = 25

24 3^{- \frac{5}{6}} \cdot 3^{- \frac{5}{6}}

- 25 - 7 x = 6 (2 x - 1)

x^{4} - 26 x^{2} + 25 \geq 0

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