What is ((1+3x^2))/((2x^2-21x+40))<0 ?

The solution to ((1+3x^2))/((2x^2-21x+40))<0 is 5/2 <x<8

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((1+3x^2))/((2x^2-21x+40))<0

\frac{( 1 + 3 x ^{2} )}{( 2 x ^{2} - 21 x + 40 )} < 0

\frac{5}{2} < x < 8

Interval Notation

(\frac{5}{2}, 8)

Decimal Notation

2.5 < x < 8

Solution steps

\frac{1 + 3 x ^{2}}{2 x ^{2} - 21 x + 40} < 0

Factor

\frac{1 + 3 x ^{2}}{2 x ^{2} - 21 x + 40} : \frac{1 + 3 x ^{2}}{( 2 x - 5 ) ( x - 8 )}

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

Identify the intervals

\frac{5}{2} < x < 8

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

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

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

\frac{( 6 - 2 x )}{( x ^{2} + 5 )} \geq 0

\frac{( x ^{3} + 1 )}{( x ^{4} + x ^{3} - 10 x ^{2} - 13 x + 21 )} > 0

What is ((1+3x^2))/((2x^2-21x+40))<0 ?
The solution to ((1+3x^2))/((2x^2-21x+40))<0 is 5/2 <x<8