Answer: Option D
[tex]3m-\frac{4}{3}-\frac{2}{m}[/tex]
Step-by-step explanation:
The initial expression is:
[tex]\frac{9m^2 - 4m - 6}{3m}[/tex]
The first step is:
[tex]\frac{9m^2}{3m} - \frac{4m}{3m} - \frac{6}{3m}[/tex]
Now we must simplify the 3 fractions.
We know that by properties of the division of exponents of the same base:
[tex]\frac{a^n}{a^h}= a^{n-h}[/tex]
Then for the expression:
[tex]\frac{9m^2}{3m}[/tex]
In this case
[tex]a=m\\n=2\\h=1[/tex]
[tex]\frac{9m^2}{3m} = 3m^{2-1}=3m[/tex]
Then for the expression:
[tex]\frac{4m}{3m}[/tex]
[tex]a=m\\n=1\\h=1[/tex]
[tex]\frac{4m}{3m}= \frac{4}{3}m^{1-1}=\frac{4}{3}[/tex]
Then for the expression:
[tex]\frac{6}{3m}[/tex]
[tex]a=m\\n=0\\h=1[/tex]
[tex]\frac{6}{3m}=\frac{2}{m}[/tex]
Finally
[tex]\frac{9m^2}{3m} - \frac{4m}{3m} - \frac{6}{3m}=3m-\frac{4}{3}-\frac{2}{m}[/tex]
