What is the first step to simplify (7u^3 + 11)/(u^3-u^2) in a homework question?

[Puchinita5]

Homework Statement

see link: https://www.webassign.net/latex2pdf/a577e8c682b39448d3e71b75b95ff053.pdf

This shows the problem and solution for a homework question.

Maybe I'm just not seeing it, but I totally don't understand the first step. How did they make (7u^3 + 11)/(u^3-u^2) equal to [7+ (7u^2 + 11)/(u-1)u^2] ?

I just don't see what math trick was used. I understand the denominator just pulled a u^2 out, but mainly i don't see where how the 7 was taken out.

I have a feeling I will slap my forehead when someone explains it to me, but I just can't figure it out.

Thank you,
Puch

Homework Equations

The Attempt at a Solution

 

[micromass]

Well:

$$\frac{7u^3 + 11}{u^3-u^2}=\frac{7u^3-7u^2+7u^2 + 11}{u^3-u^2}=\frac{7u^3-7u^2}{u^3-u^2}+\frac{7u^2 + 11}{u^3-u^2}=7+\frac{7u^2 + 11}{u^3-u^2}$$

Let the head-slapping begin

 

[Puchinita5]

::slaps forehead::

Thank you!

 

[Puchinita5]

on another note, what is the secret to posting on this website so that the math formulas read nicely like in your post?

 

[micromass]

Well', you'll need to know LaTeX first. Here are some links: https://www.physicsforums.com/showthread.php?t=386951

Then, whatever math you want to type: enclose it in [tex ] ... [/tex ] brackets (without the whitespace).

Also, you can double-click on any math-formula on this site to see it's code.

 

[Puchinita5]

great! Thanks so much!

 

[Mark44]

Well:

$$\frac{7u^3 + 11}{u^3-u^2}=\frac{7u^3-7u^2+7u^2 + 11}{u^3-u^2}=\frac{7u^3-7u^2}{u^3-u^2}+\frac{7u^2 + 11}{u^3-u^2}=7+\frac{7u^2 + 11}{u^3-u^2}$$

Let the head-slapping begin

Another way you can do this is by polynomial long division.