How do you solve these equations they don’t show me in my book. Once I know how to solve these I can solve the others.
(X-81)/(x-3)
(X5+y5)/(x+y)
(a3+6a2+12a+8)/ (a+2)
(5a3+8a2-23a-1)/ (5a2-7a-2)

- anonymous

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- anonymous

first one...(X-81)/(x-3)=0
x=81, 3

- anonymous

oh there was a divide sign !!!!!!! errrrrrrr

- anonymous

lets do it again

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## More answers

- anonymous

(x-9)(x+9)/x-3)
(x-3)(x+3)(x+9) /(x-3)
(x+3)(x+9)

- anonymous

ok now third one...

- anonymous

(a3+6a2+12a+8)/ (a+2)
(a+2)(a2+4a+4)/(a+2)
(a+2)^2

- anonymous

now fourth one..

- anonymous

I think I might have asked the question wrong because and I am confusing you. They want the answer to look something like this (x2 -6x +9)/ (x-3) = (x-3)

- anonymous

I've done the same too

- anonymous

not to doubt you but if you doing the same thing give the answer to (x2 +8x-16)/(x+4)

- anonymous

your question is wrong ..it should have been (x2 +8x+16)/(x+4)= (x+4)

- anonymous

the answer (x+4) is what I was look for

- anonymous

thats what I had to solve for

- anonymous

happy now??

- anonymous

noo ( again not trying to doubt your abilities) what I was checking was if your answers would look like mine. Now that I see they are what I am asking you to do is tell me the answer to the equations, because I can't see the answers your trying to give.

- anonymous

Do u want me to do any other ques?

- anonymous

sure

- anonymous

which one ?

- anonymous

I'm haveing alot of trouble with these types of questions (X5+y5)/(x+y)

- anonymous

okay..do u know long division method ???

- anonymous

yes

- anonymous

i feel u can get this one done by that..

- anonymous

I've tried but the answer keeps coming up wrong

- anonymous

'keeps coming' means u have tried more than once... haven't u ???

- anonymous

yes, but I get messed up in all the variables

- anonymous

i m going to do it on paper...I'll write the answer here...lets see what we going to get...

- anonymous

okay

- anonymous

x4-x3y+x2y2-xy3+y3

- anonymous

is that what u got?

- anonymous

no, so how did you get there

- radar

Oldnick, are the X and x the same variable

- anonymous

ahhh !!! made a lil mistake in the end...ig guess

- anonymous

no ...i think i was right...@radar whats ur thoughts??

- anonymous

@radar: yes

- anonymous

@ankur504: how did you get to your answer?

- anonymous

long division

- radar

Is this the problem as written in your text or worksheet?

- anonymous

@ankur504: yeah I now that give me the proses you used.

- anonymous

I dont know how to type that method here...sorry

- radar

\[(x ^{5}+y ^{5})/(x+y)\]

- anonymous

@ankur504: use the equation tool bar

- anonymous

wait a min..

- anonymous

@radar: the first variable looks wrong

- radar

do you mean it is not x^5???

- anonymous

##### 1 Attachment

- radar

Please restate the problem

- anonymous

look at this pic..i havent done the full problem but thats enough to give u an idea

- anonymous

@radar and @oldnick..what u have to say

- anonymous

@ankur504: I can't really see what your doing

- anonymous

i m exhausted...sry ...thats all I could do...my bad (

- amistre64

so whats our equation that we are longjohning?

- radar

\[(x+y)(x ^{4}-yx ^{3}+y ^{2}x ^{2}-y ^{3}x+y ^{4})\]

- anonymous

(X5+y5)/(x+y)

- radar

amistre64 we are trying to do (x^5+y^5/(x+Y)

- anonymous

@amistre: could you please have a look at the picture which I've uploaded top see if I m correct or not?

- amistre64

pic looks good, from what I can read :)

- radar

I think I put the factors up there the (x+y) would cancel and leave the (x^4..............y^4)

- amistre64

x^4 -x^3 y
---------------------
x+y | x^5 + y^5
-x^5 -x^4 y
---------------
-x^4 y +y^5
+x^4y +x^3 y^2
-----------------
+x^3 y^2 +y^5
and it keeps going till you get no x values to plug into it

- anonymous

@amistre64: I can't understand what you did there.

- amistre64

its just long division.... the same way you do numbers....but with xs and ys

- amistre64

les try 27/5
we want a number that is less than but close to 5*x = 27 lets use 5
5. <- when we multiply this to the 5 we "subtract" it from the 27
------
5 | 27.00000
- 25 <- 5*5 = 25....but!! 27-25 is what we want for an answer
-----
20 <- this is whats left over and drop down the next "number"

- radar

oldnick, i suggest you factor the (x^5+y^5) first using the rule \[x ^{n}+y ^{n}\] when n is odd. n is 5 so it is odd.

- anonymous

thats the problem is that the book gives an example on how to do the equation with (x3 +1)/(x+1). but not with only variables, so I don't now what to do with variables and large numbers.

- amistre64

5.4
------
5 | 27.00000
- 25
-----
20 <- now we want a number that is 5*x = 20, use 4 :)
-20 <- 5*4 = 20...but!! we want 20 - 20 for an answer..
-------
0

- anonymous

@radar: whats the xn+yn rule

- amistre64

the variables that cancel go away...and you add the ones that are alike and bring down the ones that arent....

- radar

\[(x+y)(x ^{n-1)}-yx ^{n-2}+a ^{2}x ^{n-3}-...+y ^{n-1})\] you can use this then as you see the x+y divides into the x=y giving 1 and you have the long one left which is the answer4

- amistre64

(x) * ? is close to x^5. lets use x^4
(x+y)x^4 = x^5 + x^4 y so we subtract that to get a new round
-(x^5 +x^4 y) = -x^5 -x^4 y
x^4
---------------------
x+y | x^5 + y^5
-x^5 -x^4 y <- we subtract it
---------------
0 -x^4 y +y^5 <- the x^5 goes to zero and the only things
left that didnt subtract to zero is brought
down and worked again

- radar

Corrections; change a to a y. remember in this case n=5

- amistre64

(x) * ? is close to -x^4 y. lets use -x^3 y
(x+y)-x^3 y = -x^4 y -x^3 y^2 so we subtract that to get a new round
-(-x^4 y -x^3 y^2) = x^4 y +x^3 y^2
x^4 -x^3 y
---------------------
x+y | x^5 + y^5
-x^5 -x^4 y
---------------
-x^4 y +y^5
x^4 y +x^3 y^2 <- subtract it
-----------------
0 + x^3 y^2 +y^5 <-whats left that didnt subtract
to zero is brought down and
worked again

- amistre64

thats the easiest way I know to explain it...

- amistre64

on a keyboard that is :)

- radar

The keyboard does provide limitation

- anonymous

I'm not sure if this will help but this is what they want me to do.

##### 1 Attachment

- amistre64

and that is exactly what I showed you ;)

- radar

Then the amistre64 method (long division) is the way to go

- anonymous

heres the problem what you showed me I can't understand

- amistre64

x^5 + y^5 is the same as:
x^5 +0x^4y +0x^3 y^2+0x^2 y^3+0x y^4+y^5 if you expand it out...

- anonymous

right I understand that

- amistre64

that is just impractical on the keyboard to try to use...

- amistre64

so instead of using all those 0 place holders... ignore them.

- amistre64

add together your like terms...and drop the rest down

- anonymous

okay

- anonymous

but there are no like terms

- amistre64

x^5 +0x^4 y + ............+ y^5
-x^5 -x^4 y
---------------
-x^4 y + ............. +y^5 right?

- anonymous

thats where you loss me

- amistre64

I just included the "like term" for you to see that its just a place holder

- radar

The sum of equal powers can be factored. different rules for even vs odd powers. Not really different rules, just different patterns.

- amistre64

y^5
-x^4 y
-------
-x^4 y + y^5 thats all there is to it....

- amistre64

whatever doesn subtract from each other...carries on down ....... do you see that?

- amistre64

like terms dont combine...so both terms drop down as they are..

- anonymous

what do the ------ stand for?

- amistre64

unlike terms dont combine is what it should read... my fingers got lazy on me :)

- amistre64

thats an equals bar underneath the terms to be added.
4
+5
----
9

- amistre64

we can add across like this: 4+5 = 9
or we can add up and down like this:
4
+5
----
9

- amistre64

when we do long division; we add/subtract in the vertical way.... keeps everything tidy

- amistre64

yes?no? makes sense? doesnt? i need to hear from you...

- amistre64

mind reading aint my forte :)

- anonymous

yes I understand what ---stans for now its just I was trying to figure out the problem, The problem is that the variable keep confusing me and I don't understand were the are suppose to go.

- amistre64

each time we find a "value" to multiply (x+y) by we want to choose a "value" the will make the first term disappear to zero. that way it is no longer bother in us and we can move down the line.

- amistre64

How do we make (x+y) and (x^5 + y^5) have the same first term?

- anonymous

i do not know

- amistre64

the first terms are important..... nothing else really matters. so lets concentrate on the first terms only; ok?

- amistre64

how do we get (x) to equal (x^5)..... we have to multiply it by some "value"

- amistre64

x * ? = x^5 ??

- anonymous

x^4

- amistre64

that is absolutely correct :)

- anonymous

x needs another x^4 to equal to x^5...

- amistre64

so we multiply (x+y) by (x^4) and get a "value"
what is:
x^4 (x+y) = ???

- anonymous

@ankur504: nope

- anonymous

x^5+x^4y

- amistre64

exactly :)

- amistre64

now we need to subtract that value from (x^5 + y^5) in order to move along....
what is:
-(x^5 + x^4 y ) = ???

- anonymous

I do not know

- amistre64

look at it again...what is:
-1(x^5 +x^4 y) = ??? you know this :)

- anonymous

-x^5-x^4y

- amistre64

yay!!.... I knew you knew it :)

- amistre64

now lets put this to good use shall we?
what is:
x^5 + 0x^4 y + ......... + y^5
-x^5 - x^4 y
------------------------
??? ???? ???

- anonymous

ehat do the ....... stand for

- amistre64

............. means all the garbage and space in between that gets in the way when using a keyboard.

- amistre64

its the stuff thats not important to focus on fo rthe current time

- anonymous

I thing the answer is x^5+y^5 but I might be wrong

- amistre64

lets see what happens when we combine our like terms ok? it might be easier to see for you if we do this across.

- amistre64

what does:
x^5 - x^5 = ????

- anonymous

0

- amistre64

Good :)
x^5 + 0x^4 y + ......... + y^5
-x^5 - x^4 y
------------------------
0 ???? ???
Now what is this:
0x^4 y -x^4 y = ???

- anonymous

0, but where does the other x^4y come from

- amistre64

your gonna have to be more specific...what do you mean by the "other" x^4y? the one with the 0 stuck to it? or the one with the (-) stuck to it?

- anonymous

both

- amistre64

remeber this part we did:
amistre64 Superhero (322 fans)Become a fan You're a fanNot a fan
look at it again...what is:
amistre64 Superhero (322 fans)Become a fan You're a fanNot a fan
-1(x^5 +x^4 y) = ??? you know this :)
11 minutes ago
oldnick Lifesaver (2 fans)Become a fan You're a fanNot a fan
-x^5-x^4y <----- RIGHT HERE!!!!!!!!!
10 minutes ago
amistre64 Superhero (322 fans)Become a fan You're a fanNot a fan
yay!!.... I knew you knew it :)

- amistre64

and also this part?:
amistre64 Superhero (322 fans)Become a fan You're a fanNot a fan
x^5 + y^5 is the same as:
x^5 +0x^4y +0x^3 y^2+0x^2 y^3+0x y^4+y^5 if you expand it out...
36 minutes ago

- anonymous

where does the 0x^4y come from then

- amistre64

by expanding the (x^5 + y^5) to include all the emply little spaces.

- anonymous

thats where I'm gettting lost

- amistre64

0 times any number equals 0
x+5 +0x^4 y + y^5 = x^5 + y^5 right?

- amistre64

x^5 + 0 + y^5 = x^5 + y^5 .....right?

- anonymous

yes

- amistre64

x^5 +0 +0+0+0+y^5 = x^5 + y^5 right?
alll those empty terms between x^5 ...... and .........y^5 are simply 0 terms

- anonymous

right now I need a break, I'm going to leave for right now, okay?

- amistre64

I could have written it like this jsut as well:
x^5 + y^5
-x^5 - x^4 y
-----------------------
0 ???? ???
have fun :)

- amistre64

I understand that what might seem simple for me, is not the same for someone else. But its the journey that we grow from ;)

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