What is (((x^2+x+1)(x+2)))/((x^2+4x+5))>0 ?

The solution to (((x^2+x+1)(x+2)))/((x^2+4x+5))>0 is x>-2

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(((x^2+x+1)(x+2)))/((x^2+4x+5))>0

\frac{( ( x ^{2} + x + 1 ) ( x + 2 ) )}{( x ^{2} + 4 x + 5 )} > 0

x > - 2

Interval Notation

(- 2, \infty)

Solution steps

\frac{( x ^{2} + x + 1 ) ( x + 2 )}{x ^{2} + 4 x + 5} > 0

Identify the intervals

x > - 2

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

\frac{( x ^{2} + 6 x - 11 )}{( x + 3 )} < - 1

(4 x - 5)^{2} - 16 x (x + 3) < - 21

\frac{( 2 x + 1 )}{( x ^{2} - x - 12 )} \leq \frac{1}{2}

(x + 9) (x - 3) > 0

What is (((x^2+x+1)(x+2)))/((x^2+4x+5))>0 ?
The solution to (((x^2+x+1)(x+2)))/((x^2+4x+5))>0 is x>-2