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

The solution to (((x-1)(x-2)))/(((x+1)(x+2)))>0 is x 2

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(((x-1)(x-2)))/(((x+1)(x+2)))>0

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

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

Interval Notation

(- \infty, - 2) \cup (- 1, 1) \cup (2, \infty)

Solution steps

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

Identify the intervals

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

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

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

\frac{( 2 x ^{2} + 3 x + 5 )}{( 2 x ^{2} + 8 x + 1 )} \leq 0

\frac{( x ^{2} - 3 x + 7 )}{( x ^{2} + 1 )} < 1

\frac{13}{( x - 3 )} < 0

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