Melody

Thanks Guys - both these answers have great value. 

I have added this question to reference material.

Definitely pecan    yum

5x/x^2-x-6 + 7/7^2+4x+4

$$\\(5x/x^2)-x-6 + (7/7^2)+4x+4\\
5/x-x-6 + 1/7+4x+4\\
5/x+3x-2 + 1/7\\
5/x+3x-(1 + 6/7)\\
5/x+3x-13/7\\$$

$$\frac{x}{2}$$

It is best to think of normal numbers first and see what happens

judy has 80 peices   Wendy has 10 peices less.   That is 70 peicse to Wendy

if Judy gives Wendy 5 peices than they will both have 75 peices

5=10/2

Yes of course you are correct Chris.    I must have been suffering a major CDD recurrence.   

This site might help you?

http://stattrek.com/online-calculator/binomial.aspx

$$\left({\frac{{\mathtt{\pi}}}{{\mathtt{180}}}}\right){\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left(-{\mathtt{1}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{3.14}} = {\mathtt{2.354\: \!601\: \!836\: \!602\: \!551\: \!7}}$$

$$\left({\frac{{\mathtt{\pi}}}{{\mathtt{180}}}}\right){\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left(-{\mathtt{1}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{\pi}} = {\mathtt{2.356\: \!194\: \!490\: \!192\: \!344\: \!9}}$$

i used this calc and i get   2.356

--------------------------

now without a calc

atan(-1)+pi   =  -pi/4 + pi = 3pi/4

$${\frac{{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{\pi}}}{{\mathtt{4}}}} = {\mathtt{2.356\: \!194\: \!490\: \!192\: \!344\: \!9}}$$

$$\\4500(1+0.032)^n>5000\\\\
(1+0.032)^n>\frac{10}{9}\\\\
log(1.032)^n>log\frac{10}{9}\\\\
nlog(1.032)>log\frac{10}{9}\\\\
n>\frac{log\frac{10}{9}}{log(1.032)}\\\\$$

$${\frac{{log}_{10}\left({\frac{{\mathtt{10}}}{{\mathtt{9}}}}\right)}{{log}_{10}\left({\mathtt{1.032}}\right)}} = {\mathtt{3.344\: \!919\: \!817\: \!058\: \!767\: \!9}}$$

$$\\n>3.3 years\\
n=4\;\;years$$

What you have is not a formula with a standardised name.  It is just the expansion for a perfect square.

quadratic formula   (it should have x = out the front like anon has written.)

It is just

$$\frac{x+2}{(x-2)^2}$$

and this cannot be simplified