Answer:
[tex]\dfrac{-5x^2+34x-32}{x^2-10x+24}[/tex]
Step-by-step explanation:
Write each fraction using a common denominator, then combine numerators and collect terms. "Simplify" usually means "eliminate parentheses."
[tex]\dfrac{8}{x-4}-\dfrac{4}{x-6}-\dfrac{5x}{x-4}=\dfrac{8(x-6)}{(x-4)(x-6)}-\dfrac{4(x-4)}{(x-4)(x-6)}-\dfrac{5x(x-6)}{(x-4)(x-6}\\\\=\dfrac{8(x-6)-4(x-4)-5x(x-6)}{(x-4)(x-6)}=\dfrac{8x-48-4x+16-5x^2+30x}{(x-4)(x-6)}\\\\=\boxed{\dfrac{-5x^2+34x-32}{x^2-10x+24}}[/tex]
