Question

The first step when dividing 9m2 − 4m − 6 by 3m is shown.

(9m^2 divided by 3m)-(4m divided by 3m)-(6 divided by 3m)
Which could be the next step?
(A) 3m-3/4-m/2
(B) 3m-3/4-2/m
(C) 3m-4/3-m/2
(D) 3m-4/3-2/m

Answer 1

Answer: Option D

`3m-(4)/(3)-(2)/(m)`

Explanation:

The initial expression is:

`(9m^2 - 4m - 6)/(3m)`

The first step is:

`(9m^2)/(3m) - (4m)/(3m) - (6)/(3m)`

Now we must simplify the 3 fractions.

We know that by properties of the division of exponents of the same base:

`(a^n)/(a^h)= a^(n-h)`

Then for the expression:

`(9m^2)/(3m)`

In this case

`a=m\\n=2\\h=1`

`(9m^2)/(3m) = 3m^(2-1)=3m`

Then for the expression:

`(4m)/(3m)`

`a=m\\n=1\\h=1`

`(4m)/(3m)= (4)/(3)m^(1-1)=(4)/(3)`

Then for the expression:

`(6)/(3m)`

`a=m\\n=0\\h=1`

`(6)/(3m)=(2)/(m)`

Finally

`(9m^2)/(3m) - (4m)/(3m) - (6)/(3m)=3m-(4)/(3)-(2)/(m)`