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}

- 3 x^{2} - 4 x - 1

10 = \frac{p}{10}

12 x^{2} + 25 x + 12 = 0

(x + 5)^{2} = - 36

14 = \frac{a}{2}

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