#### Answer

$f^{-1}(x) = \frac{x - 3}{2 + 5x}$

#### Work Step by Step

$f(x) = \frac{2x +3}{1 - 5x}$
$y = \frac{2x +3}{1 - 5x}$
y(1- 5x) = 2x + 3
y - 5xy = 2x + 3
y - 3 = 2x + 5xy
y - 3 = x(2 + 5y)
$x = \frac{y - 3}{2 + 5y}$
$f^{-1}(x) = \frac{x - 3}{2 + 5x}$