What is ((x-1))/((4x+5))<((x-3))/((4x-3)) ?

The solution to ((x-1))/((4x+5))<((x-3))/((4x-3)) is -5/4 <x< 3/4

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((x-1))/((4x+5))<((x-3))/((4x-3))

\frac{( x - 1 )}{( 4 x + 5 )} < \frac{( x - 3 )}{( 4 x - 3 )}

- \frac{5}{4} < x < \frac{3}{4}

Interval Notation

(- \frac{5}{4}, \frac{3}{4})

Decimal Notation

- 1.25 < x < 0.75

Solution steps

\frac{x - 1}{4 x + 5} < \frac{x - 3}{4 x - 3}

Rewrite in standard form

\frac{1}{( 4 x + 5 ) ( 4 x - 3 )} < 0

\frac{1}{a} < 0

then

a < 0

(4 x + 5) (4 x - 3) < 0

Identify the intervals

- \frac{5}{4} < x < \frac{3}{4}

(x - 3) (x + 1) < 0

- x^{2} \geq 0

x - 17 \geq \frac{60}{x}

\frac{( x ^{2} + 2 x - 19 )}{( x - 4 )} > 4

7 x^{2} > 14 x

What is ((x-1))/((4x+5))<((x-3))/((4x-3)) ?
The solution to ((x-1))/((4x+5))<((x-3))/((4x-3)) is -5/4 <x< 3/4