#### Answer

$\dfrac{2x-5}{6x+9}-\dfrac{4}{2x^{2}+3x}=\dfrac{x-4}{3x}$

#### Work Step by Step

$\dfrac{2x-5}{6x+9}-\dfrac{4}{2x^{2}+3x}$
Take out common factor $3$ from the denominator of the first fraction and common factor $x$ from the denominator of the second fraction:
$\dfrac{2x-5}{6x+9}-\dfrac{4}{2x^{2}+3x}=\dfrac{2x-5}{3(2x+3)}-\dfrac{4}{x(2x+3)}=...$
Evaluate the substraction:
$...=\dfrac{(2x-5)x-4(3)}{3x(2x+3)}=\dfrac{2x^{2}-5x-12}{3x(2x+3)}=...$
Factor the numerator and simplify:
$...=\dfrac{(2x+3)(x-4)}{3x(2x+3)}=\dfrac{x-4}{3x}$