Answer:
[tex]( f - g)(x) = \frac{2x - \sqrt{x} + 14 }{3x}[/tex]
Step-by-step explanation:
[tex]f(x) = \frac{2x + 6}{3x} \\ \\ g(x) = \frac{ \sqrt{x} - 8}{3x} [/tex]
To find ( f - g)(x) , subtract g(x) from f(x)
That's
[tex]( f - g)(x) = \frac{2x + 6}{3x} - \frac{ \sqrt{x} - 8}{3x} [/tex]
Since they have a common denominator that's 3x we can subtract them directly
That's
[tex] \frac{2x + 6}{3x} - \frac{ \sqrt{x} - 8}{3x} = \frac{2x + 6 - ( \sqrt{x} - 8) }{3x} \\ = \frac{2x + 6 - \sqrt{x} + 8 }{3x} \\ = \frac{2x - \sqrt{x} + 6 + 8 }{3x} [/tex]
We have the final answer as
[tex]( f - g)(x) = \frac{2x - \sqrt{x} + 14 }{3x} [/tex]
Hope this helps you
