Given:
[tex]\begin{gathered} m(x)\text{ =}\frac{57}{28}x^2\text{ -}\frac{9}{8}x\text{ - }\frac{10}{6} \\ n(x)\text{ = }\frac{10}{6}x\text{ - }\frac{8}{9} \end{gathered}[/tex]
We are required to find the function p(x) that describes the difference between m(x) and n(x)
The function p(x) is:
[tex]\begin{gathered} p(x)\text{ =m\lparen x\rparen - n\lparen x\rparen} \\ =\frac{57}{28}x^2\text{ -}\frac{9}{x}x\text{ - }\frac{10}{6}\text{ -\lparen}\frac{10}{6}x\text{ -}\frac{8}{9}) \\ =\text{ }\frac{57}{28}x^2\text{ - }\frac{9}{8}x\text{ -}\frac{10}{6}\text{ - }\frac{10}{6}x\text{ +}\frac{8}{9} \end{gathered}[/tex]
Simplifying further:
[tex]\begin{gathered} p(x)=\frac{57}{28}x^2\text{ -}\frac{9}{8}x\text{ -}\frac{10}{6}x\text{ -}\frac{10}{6}\text{ + }\frac{8}{9} \\ =\text{ }\frac{57}{28}x^2\text{ -}\frac{27x-40x\text{ }}{24}\text{ + }\frac{-90\text{ + 48}}{54} \\ =\text{ }\frac{57}{28}x^2\text{ -}\frac{67x}{24}\text{ -}\frac{42}{54} \\ =\text{ }\frac{57}{28}x^2\text{ -}\frac{67}{24}x\text{ -}\frac{7}{9} \end{gathered}[/tex]
Answer: Option A
