## Algebra: A Combined Approach (4th Edition)

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