What is x/((x-3))< 9/((4x+3)) ?

The solution to x/((x-3))< 9/((4x+3)) is -3/4 <x<3

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x/((x-3))< 9/((4x+3))

\frac{x}{( x - 3 )} < \frac{9}{( 4 x + 3 )}

- \frac{3}{4} < x < 3

Interval Notation

(- \frac{3}{4}, 3)

Decimal Notation

- 0.75 < x < 3

Solution steps

\frac{x}{x - 3} < \frac{9}{4 x + 3}

Rewrite in standard form

\frac{4 x ^{2} - 6 x + 27}{( x - 3 ) ( 4 x + 3 )} < 0

Identify the intervals

- \frac{3}{4} < x < 3

\frac{( x - 4 )}{( x + 2 )} \geq \frac{( x - 5 )}{( x + 4 )}

x^{3} + 9 x^{2} \leq - 26 x - 24

x, f < - 8

x^{2} > 4 (8 - x)

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

What is x/((x-3))< 9/((4x+3)) ?
The solution to x/((x-3))< 9/((4x+3)) is -3/4 <x<3