The range of values of x for which the inequality $\frac{x-1}{4x+5}<\frac{x-3}{4x-3}$  holds is

The given inequation is$\frac{x-1}{4x+5}<\frac{x-3}{4x-3}$

$\Rightarrow \frac{x-1}{4x+5}-\frac{x-3}{4x-3}<0$

$\Rightarrow \frac{\left(x-1\right)\left(4x-3\right)-\left(x-3\right)\left(4x+5\right)}{\left(4x+5\right)\left(4x-3\right)}<0$

$\Rightarrow \frac{18}{\left(4x+5\right)\left(4x-3\right)}<0$

$\Rightarrow \left(4x+5\right)\left(4x-3\right)<0$

$\Rightarrow 4x+5<0\text{ , }4x-3<0$

$\Rightarrow x\in \left(\frac{-5}{4},\frac{3}{4}\right)$