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

The solution to x/(x+2)+1/(x-1) 2

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

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

x < - 5 or - 2 < x < 1 or x > 2

Solution steps

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

Rewrite in standard form

\frac{- x ^{2} - 3 x + 10}{( x + 2 ) ( x - 1 )} < 0

Factor

\frac{- x ^{2} - 3 x + 10}{( x + 2 ) ( x - 1 )} : \frac{- ( x - 2 ) ( x + 5 )}{( x + 2 ) ( x - 1 )}

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

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x - 2 ) ( x + 5 ) ) ( - 1 )}{( x + 2 ) ( x - 1 )} > 0 \cdot (- 1)

Simplify

\frac{( x - 2 ) ( x + 5 )}{( x + 2 ) ( x - 1 )} > 0

Identify the intervals

x < - 5 or - 2 < x < 1 or x > 2

8 a^{2} b^{3} - 4 a^{2} b^{2}

x^{2} - 10 x + 41 = 0

2 (y + 1) + 4 y = 3 (2 y - 1) + 8

- 38 d - 57 \geq - 19 d + 76

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