[tex] \dfrac{4-\frac{12}{2x-3}}{5+\frac{15}{2x-3}}=\dfrac{\frac{4(2x-3)}{2x-3}-\frac{12}{2x-3}}{\frac{5(2x-3)}{2x-3}+\frac{15}{2x-3}}=\dfrac{\frac{8x-12-12}{2x-3}}{\frac{10x-15+15}{2x-3}}=\dfrac{\frac{8x-24}{2x-3}}{\frac{10x}{2x-3}}=\\\\\\=\dfrac{8x-24}{2x-3}\cdot\dfrac{2x-3}{10x}=\dfrac{8x-24}{10x}=\boxed{\frac{4x-12}{5x}} [/tex]
