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

The solution to ((x^2+2x-3))/((x^2+1))<0 is -3<x<1

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((x^2+2x-3))/((x^2+1))<0

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

- 3 < x < 1

Interval Notation

(- 3, 1)

Solution steps

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

Factor

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

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

Identify the intervals

- 3 < x < 1

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

\frac{( ( x ^{2} - 5 ) ( x ^{2} - 4 ) )}{( x - 1 )} \leq 0

\frac{( x ^{2} - 5 x + 12 )}{( x ^{2} - 4 x + 5 )} > 3

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

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

What is ((x^2+2x-3))/((x^2+1))<0 ?
The solution to ((x^2+2x-3))/((x^2+1))<0 is -3<x<1