What is (15x^2-23x-28)/(5x^2-6x-8)<0 ?

The solution to (15x^2-23x-28)/(5x^2-6x-8)<0 is 2<x< 7/3

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(15x^2-23x-28)/(5x^2-6x-8)<0

\frac{15 x ^{2} - 23 x - 28}{5 x ^{2} - 6 x - 8} < 0

2 < x < \frac{7}{3}

Interval Notation

(2, \frac{7}{3})

Decimal Notation

2 < x < 2.33333 \dots

Solution steps

\frac{15 x ^{2} - 23 x - 28}{5 x ^{2} - 6 x - 8} < 0

Factor

\frac{15 x ^{2} - 23 x - 28}{5 x ^{2} - 6 x - 8} : \frac{( 5 x + 4 ) ( 3 x - 7 )}{( 5 x + 4 ) ( x - 2 )}

\frac{( 5 x + 4 ) ( 3 x - 7 )}{( 5 x + 4 ) ( x - 2 )} < 0

Identify the intervals

2 < x < \frac{7}{3}

2 (\frac{x}{2} + \frac{3}{2}) = 2.8

8 (2 - x) = 0

21 x^{2} + 30 x - 24

- x (x^{2} + 1)^{- 2} (2 x) + (x^{2} + 1)^{- 1}

∣ x - 1 ∣ = ∣ 3 x + 6 ∣

What is (15x^2-23x-28)/(5x^2-6x-8)<0 ?
The solution to (15x^2-23x-28)/(5x^2-6x-8)<0 is 2<x< 7/3