subtract: y/y-2 - 8+y/2-y

- anonymous

subtract: y/y-2 - 8+y/2-y

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- anonymous

This is tricky... you need to know this fact.
2 - y = -(y - 2)
you can always flip numbers around a - sign and multiply by a -
so 5 - x = -(x - 5)

- anonymous

In this case you want the 2 - y to be y - 2 because you need a common denominator.
so you turn the bottom in to y - 2 and then you put a - sign out in front...
In this case that negative sign out front would turn your problem into a + sign
y/y-2 + 8 + y/y - 2
Now you have common denominators
y + 8 + y
--------
y - 2
2y + 8
------
y - 2

- anonymous

omg hi again!!!

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- anonymous

this was our next question

- anonymous

OK... I just found you...
do you get this?

- anonymous

i dont understand how you get the common denom....

- anonymous

Well... y - 2 and 2 - y are opposites of each other....
you should be able to see that if you flip the one on the right around the minus sign it becomes the y - 2 ex. 2 - y flips to y - 2
OK?

- anonymous

then you have to change the subtraction to addition??

- anonymous

Yes... because it is the opposite you have to put a - sign out in front, and actually you change the sign of the problem... so in this case the subtraction becomes addition.
This is a hard concept.

- anonymous

hmmm then what

- anonymous

Then you have a common denominator... so if you look above to my steps you will see that you put everything on the top over y - 2 because you now have a common denominator

- anonymous

7/T-2 - 6/T^2-2T - 3/T is the LCD T^2-2T?

- anonymous

7 6 3
---- - ----------- - ------
T - 2 T^2 - 2T T
T - 2 factors into (T - 2)
T^2 - 2T factors into T(T - 2)
T factors into T
Common denominator is T(T - 2) or T^2 - 2T easier if you write it T(T - 2)

- anonymous

T(T - 2) * 7 T(T - 2) * 6 T(T - 2) * 3
------------ - ---------- - ----------
(T - 2) T(T - 2) T

- anonymous

The (T - 2)'s cancel in the first fraction
The T and (T - 2) cancel in the second fraction
The T cancels in the third fraction

- anonymous

7t-6-3t-2 ??

- anonymous

7T - 6 - 3(t - 2)
7T - 6 - 3T + 6
4T

- anonymous

isnt it -6?

- anonymous

left with 4t-12

- anonymous

The - sign goes with the 3 so it is actually
-3(T - 2)
and -3 * -2 = +6

- anonymous

ohhh got it

- anonymous

meeee tooooooo!

- anonymous

YEAH!!!!!

- anonymous

5-x/x-1 / 2-x/x+1

- anonymous

5 - x 2 - x
---- divided by -----
x - 1 x + 1
write the divide sign that has a --- with a dot above and below.
Are you sure this is what you want.

- anonymous

noooo wait hold on

- anonymous

X
5- ----
X-1
___________
X
2- ----
X+1

- anonymous

yes!

- anonymous

OK... First we will simplify the top.
5 x
- - ----
1 x- 1
what is the common denominator?

- anonymous

x-1?

- anonymous

(x - 1)*5 x
------- - -----
x - 1 x - 1

- anonymous

5x - 5 x
----- - -----
x - 1 x - 1
4x - 5
------
x - 1
ok?

- anonymous

5X+1-X
---------
X-1

- anonymous

GOT IT

- anonymous

Yes... now add the x's

- anonymous

Now let's do the same to the bottom.

- anonymous

X+2
-----
X+1

- anonymous

2 x
- - ----
1 x + 1
(x + 1)*2 x
-------- - ----
(x + 1)*1 x + 1
(x + 1) *2 x
-------- - -----
x + 1 x + 1
2x + 2 - x
---------
x + 1
x + 2
----
x + 1

- anonymous

OOPS... go back to the first one... you have 4x - 1 look at mine... it is 4x - 5.. you have to distribute.

- anonymous

got it

- anonymous

4x - 5 x + 2
------ divided by ------
x - 1 x + 1
Now.... when ever you have a fraction divided by a fraction.
you ALWAYS multiply by the reciprocal

- anonymous

4X+5
------
X+1
--------
X+2
---
X+1

- anonymous

4x - 5 x + 1
------ x -----
x - 1 x + 2

- anonymous

top right and bottom left cancel out?

- anonymous

4X+5
------
X+2

- anonymous

amazing... go back and look at the numerator.. it is 4x - 5

- anonymous

4X-5
------
X+2
????? I HOPE

- anonymous

I wish they did cancel... they usually do.. but not here a (x - 1) can ONLY cancel with an (x - 1)
and a (x + 1) can ONLY cancel with (x + 1)
Usually you CAN cancel, but not in this problem.
You would multiply the numerators (FOIL METHOD)
then multiply the denominators (FOIL METHOD)
and you would have your answer

- anonymous

so now what!?!?!!? omg im lost now

- anonymous

(4x - 5)(x + 1)
-------------
(x - 1)(x + 2)
4x^2 + 4x - 5x - 5
----------------
x^2 + 2x - x - 2
4x^2 - x - 5
-----------
x^2 + x - 2

- anonymous

Unless you did not type in the original problem correctly? otherwise this is the answer.

- anonymous

i got that

- anonymous

Good.

- anonymous

i wanna cry this is hard

- anonymous

solve for X: (4x-7)^2 = -27 :)

- anonymous

They are just a lot of steps.

- anonymous

(4x - 7)^2 = -27
Are you sure this is correct?

- anonymous

Yes

- anonymous

yessssssssss

- anonymous

OK.. so you know what imaginary numbers are i's

- anonymous

yes !

- anonymous

OK.. what if I gave you this problem... do you know what to do.
x^2 = 16

- anonymous

yes square root both sides

- anonymous

Good... so in this problem you have
(something)^2 = -27
so you square root both sides

- anonymous

x=4

- anonymous

(4x - 7)^2 = -27
4x - 7 = sqrt(-27)

- anonymous

sqrt(-27) is -3i sqrt(3)
do you understand this?

- anonymous

\[3i \sqrt{3?}\]

- anonymous

yess!

- anonymous

OOPS you are correct is is positive

- anonymous

4x - 7 = 3i sqrt(3)
4x = 3i sqrt(3) + 7
x = 3i sqrt(3) + 7
------------
4

- anonymous

\[9+3x-2x ^{2} \over x ^{2}-16 \]

- anonymous

wait im not done hold on!

- anonymous

all that divided by \[4x ^{3}-9x \over 2x ^{2}+5x-12\]

- anonymous

simplify and state restricitons

- anonymous

-2x^2 + 3x + 9 2x^2 + 5x - 12
--------------- x -------------
x^2 - 16 4x^3 - 9x
since it is a fraction divide by a fraction.. we are going to turn it into a multiply problem right away by using the reciprocal.
OK?

- anonymous

ok hold on lemme take all that in

- anonymous

then factor?

- anonymous

yes we have to factor all four... but it is difficult to factor when there is a negative in front of the x^2 so for the first fraction in the numerator we are going to factor out a - sign first.
- (2x^2 - 3x - 9)

- anonymous

-(2x + 3)(x - 3) (2x - 3)(x + 4)
-------------- x -------------
(x + 4)(x - 4) x(4x^2 - 9)
x(2x + 3)(2x - 3)

- anonymous

-(2x+3)(x-3) (x+4) (2x-3)
---------- ------------
(x+4) (x-4) x(2x+3) (2x-3)

- anonymous

now we can cancel out right?

- anonymous

Yes... now cancel anything in ( )'s with like ( )'s
Anything on the top with anything on the bottom that matches.

- anonymous

x-3
-----
x(x-4)

- anonymous

close you still have that - sign on top
-(x - 3)
-------
x(x - 4)
they may want it like
-x + 3
------
x^2 - 4x
it is all the same...

- anonymous

Now you also said you had to tell restrictions.

- anonymous

yesss

- anonymous

OK... go back to the factored fractions.
The rule is you can NEVER divide by 0 so whatever makes those ( )'s 0 would be a restriction.

- anonymous

We are only concerned with the denominators.

- anonymous

okkk

- anonymous

(x + 4)(x - 4) x(2x + 3)(2x - 3)

- anonymous

-4,4 -3/2, 3/2

- anonymous

And one more you need 0 because of the single x
Every where there is an x there is a restriction.

- anonymous

blexting you are great!!! we have 3 more can we keep going?

- anonymous

Sure

- anonymous

way better then our professor!

- anonymous

X^2-9
----------------
X^3+X^2-9X-9
SIMPLIFY

- anonymous

Factor

- anonymous

(x + 3)(x - 3)
------------

- anonymous

When you have 4 terms you should try this first.
Take the first two terms and take out a common factor.
x^3 + x^2 = x^2(x + 1)
Take the last two terms and do the same thing.
-9x - 9 = -9(x + 1)
OK?

- anonymous

x+1 is the answer right?

- anonymous

(X^2-9) (X+1)

- anonymous

I MEAN (X-1)

- anonymous

OK.. Now you have x^2(x + 1) - 9(x + 1) ... good amozing.
because (x + 1) is a common factor you now have
(x + 1)(x^2 - 9) BUT this is the difference of two squares.
(x + 1)(x + 3)(x - 3)

- anonymous

they dont cancel out

- anonymous

?

- anonymous

So you have the top which is
(x + 3)(x - 3)
------------
(x + 1)(x + 3)(x - 3)
then cancel
and you are left with
1
-------
x + 1
with restrictions of x cannot be -1,-3 or 3

- anonymous

solve for X: 3 17 7
------- = ---- - -----
4x+2 2 2x+1

- anonymous

Common denominator
4x + 2 = 2(2x + 1)
2 = 2
2x + 1 = 2x + 1
common denominator 2(2x + 1)

- anonymous

Put that on top of each fraction and then cancel with the denominators.

- anonymous

2(2x + 1) * 3 2(2x + 1) * 17 2(2x + 1) * 7
----------- = ------------- - -----------
2(2x + 1) 2 2x + 1

- anonymous

34X+3=3
??

- anonymous

X=1/34

- anonymous

3 = 17(2x + 1) - 14
3 = 34x + 17 - 14
3 = 34x + 3
0 = 34x
0 = x

- anonymous

amozing when you take 34x + 3 = 3 and you subtract 3 you get 34x = 0

- anonymous

Restrictions x cannot be -1/2

- anonymous

GOT IT, THANKS!!
ONE MORE :)

- anonymous

OK

- anonymous

X^2+XY-2Y^2 X
----------- X -----------------
X^3+X^2Y X^2+3XY+2Y^2

- anonymous

3X^3Y^2

- anonymous

NOT 3Y JUST Y SORRY

- anonymous

(x + 2y)(x - y) x
------------ times --------------
x^2(x + y) (x + 2y)(x + y)

- anonymous

(x - y)
------------
x(x + y)^2

- anonymous

GOT IT THANKS!!

- anonymous

gixxergirl..... did you leave us?

- anonymous

Are we done????

- anonymous

lol sorry i had to pee!!! but thank you so mucchhhhh for everythinggg !!! are you a math teacher?

- anonymous

yes I am in a high school

- anonymous

YOU HAVE BEEN SO HELPFUL!! THANK YOU SO MUCH

- anonymous

No problem.. if you see me on here again and want help.. just holler.
Have a wonderful Easter...
He is risen!!!
Good night.

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