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I know. The teacher said, " try your best. I will tell you how on Friday" 

so, I try to make the best work I can. Ok. I know. It is not my level, but thanks for helping.

(x^2-2011x+1)/x=0/x

x-2011+1/x=0

x+1/x=2011

x-1+1/x=2011-1=2010

Good job.Is it funny or not to do problem like this?if yes, i will put a problem everyday to the forum 

I'll put it down to your "left-handedness".............LOL!!!!!

Much of this is WAY OVER your head Dragon.  Your teacher cannot seriously expect you to do it!!

I don't have any "magic" formula for doing these, DS......it's mainly just factoring and "cancelling"......plus a few algebraic "tricks".......

I thought about the restriction Chris but I didn't put it there because the first statement would not be true if x=0.

But like always - yours is shorter.

I started mine from the previous result where the question was wrong.

That is my excuse and I am sticking with it!  LOL  

x² = 2011x - 1  →  x² + 1 = 2011x

So

x^2-2010x+【2011/(x^2+1)] =

[2011x - 1 ] - 2010x + 2011/(2011x) =

x - 1 + 1/x =

[x² - 1x + 1] / x =

[x² + 1 - x ] /x =

[2011x - x] / x =

2010x / x =

2010      (with the restriction that x ≠ 0)

I am glad that you find me entertaining Dragon.  

Thank you! I need to understand what to do for other similar questions like that one. Can you please tell or explain what to do in questions like these?

thanks. I would give you hundreds and hundreds of points CPhill.

Melody. Lol! That was so funny.

No I think i am happy enough with that answer.   

$$\\If\;\; x^2-2011x+1=0 $ is true, then what is the value of $\\\\
x-2010x+\frac{2011}{(x^2+1)}\;\;?\\\\
$first$\\
x^2-2011x+1=0\\
x^2+1=2011x\\\\
$now$\\\\\
x^2-2010x+\frac{2011}{(x^2+1)}\\\\
=x^2-2010x+\frac{2011}{(2011x)}\\\\
=x^2-2010x+\frac{1}{x}\\\\
=(x^2+1)-1-2010x+\frac{1}{x}\\\\
=2011x-1-2010x+\frac{1}{x}\\\\
=x-1+\frac{1}{x}\\\\$$

$$\\=\frac{x^2-x+1}{x}\\\\
=\frac{1011x-x}{x}\\\\
=\frac{1010x}{x}\\\\
=1010$$

I think I might have stuffed up somewhere.  Plus I have a reputation for doing things the LONG way.

I'm going to look over it some more.   

3a³(16- a²) / [12a⁶ (a² - 9a + 20)]   factoring everything, we have

3a³ (4 - a)(4+a) /[ 12a⁶ (a - 4)(a-5)] =

-(1/4a³ )(a-4)(a+4)/[(a-4)(a-5)] =   (we can factor a "-" out of (4 - a) = - (a - 4))

-(1/4a³)(a+4)/(a-5) = (5-a)(4+a)/(4a³)

x^2-2010x+【2011/(x^2+1)]

Maybe you really mean this ??

 (x^2-2010x+2011) /(x^2+1)

Is that right?

If 790 is in feet, we have

790/9 = 87.7 ft per min = 1.462 ft per second

Note that, every minute, the wheel rotates through 40° of arc

oh. i am sorry the second equation should be x^2-2010x+2011/(x^2+1)

$$\\If\;\; x^2-2011x+1=0 $ is true, then what is the value of $\\\\
x-2010x+\frac{2011}{(x^2+1)}\;\;?\\\\
$first$\\
x^2-2011x+1=0\\
x^2+1=2011x\\\\
$now$\\\\\
x-2010x+\frac{2011}{(x^2+1)}\\\\
=x-2010x+\frac{2011}{(2011x)}\\\\
=x-2010x+\frac{1}{x}\\\\
=-2009x+\frac{1}{x}\\\\$$

Maybe you needed more brackets in your question?  I think that you probably did.  

Todo esto esta confudido. El approxamation es:

$${\mathtt{\,-\,}}{\frac{{\mathtt{101}}}{{{\mathtt{115}}}^{{\mathtt{684}}}}} = {\mathtt{\,-\,}}{\frac{{\mathtt{101}}}{\infty}}$$

$$Approxamation:\;\boxed{-\dfrac{101}{\infty}}$$

I don't know - can anyone help?

2 is known as windows. Why is 2 known as windows? I asked my teacher, but i never understood her.

product means multiply, Sum means plus

I think that you mean

What are 2 numbers whose Product of +48 sum of-14

The product is positive so the numbers have to have the same sign

The sum is negative so they both have to be negative

that is easy then  -6 and -8

If you go through this logic it makes it much easier!    

Huh ???????

$$\frac{5x}{6}\div \frac{-1}{2}\\\\
\frac{5x}{6}\times \frac{2}{-1}\\\\
\frac{5x}{6}\times \frac{-2}{1}\\\\
\frac{-10x}{6}\\\\
\frac{-5x}{3}\\\\$$

We have two vectors here, v₁ and v₂

v₁ = <165cos180, 165sin180>  and v₂ = <95cos(225), 95sin(225)>

Summing the "x" components we have

165cos(180) + 95cos(225) = about -232.18

Summing the "y" components we have

165sin(180) + 95sin(225) = about -67.18

And the magnitude is given by   √[(-232.18)² + (-67.18)²] = about 241.7 km

And the direction is given by

tan^-1 (-67.18/-232.18) = about 16.14° in the 3rd quadrant = about 196.14°