How do you simplify the expression #(12m^4-24m^3+6m^2+9m-9)/(6m^2)#?

2 Answers
Jun 12, 2017

Answer:

#1/2m^2-5/2m+1#

Explanation:

Let's start with the original problem:

#(12m^4-24m^3+6m^2+9m-9)/(6m^2)#

We can rewrite the expression like so:

#(12m^4)/(6m^2)-(24m^3)/(6m^2)+(6m^2)/(6m^2)+(9m)/(6m^2)-9/(6m^2)#

Now we can simplify each of the terms in the expression:

#2m^2-4m+1+(3/2)m^-1-3/(2m^2)#

We can get rid of the negative exponent:

#2m^2-4m+1+3/(2m)-3/(2m^2)#

We then rearrange the expression from the highest power to the lowest power and combine like terms:

#2m^2-3/(2m^2)-4m+3/(2m)+1#

#1/2m^2-5/2m+1#

Hope this helped!

Jun 12, 2017

Answer:

#(12m^4-24m^3+6m^2+9m-9)/(6m^2)=color(blue)((4m^4-8m^3+2m^2+3m-3)/(2m^2)#

Explanation:

Simplify:

#(12m^4-24m^3+6m^2+9m-9)/(6m^2)#

Factor out the common factor #3# in the numerator.

#(3(4m^4-8m^3+2m^2+3m-3))/(6m^2)#

Divide #6# in the denominator by #3# in the numerator.

#(color(red)cancel(color(black)(3^1))(4m^4-8m^3+2m^2+3m-3))/(color(red)cancel(color(black)(6^2))m^2)#

Simplify.

#(4m^4-8m^3+2m^2+3m-3)/(2m^2)#