What is ((x^2-7x+12))/((2x^2+4x+5))> 1/2 ?

The solution to ((x^2-7x+12))/((2x^2+4x+5))> 1/2 is x< 19/18

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((x^2-7x+12))/((2x^2+4x+5))> 1/2

\frac{( x ^{2} - 7 x + 12 )}{( 2 x ^{2} + 4 x + 5 )} > \frac{1}{2}

x < \frac{19}{18}

Interval Notation

(- \infty, \frac{19}{18})

Decimal Notation

x < 1.05555 \dots

Solution steps

\frac{x ^{2} - 7 x + 12}{2 x ^{2} + 4 x + 5} > \frac{1}{2}

Rewrite in standard form

\frac{- 18 x + 19}{2 x ^{2} + 4 x + 5} > 0

Identify the intervals

x < \frac{19}{18}

\frac{( x ^{4} )}{( ( x - 2 ) ^{2} )} > 0

\frac{( ( x - 1 ) ( x - 5 ) )}{( x - 3 )} > 0

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

\frac{1}{x} < \frac{2}{( x - 2 )}

x^{4} - x^{2} < 0

What is ((x^2-7x+12))/((2x^2+4x+5))> 1/2 ?
The solution to ((x^2-7x+12))/((2x^2+4x+5))> 1/2 is x< 19/18