Question

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

Answer 1

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)

Answer 2

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

Answer 3

omg hi again!!!

Answer 4

this was our next question

Answer 5

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

Answer 6

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

Answer 7

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?

Answer 8

then you have to change the subtraction to addition??

Answer 9

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.

Answer 10

hmmm then what

Answer 11

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

Answer 12

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

Answer 13

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)

Answer 14

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

Answer 15

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

Answer 16

7t-6-3t-2 ??

Answer 17

7T - 6 - 3(t - 2)

7T - 6 - 3T + 6

4T

Answer 18

isnt it -6?

Answer 19

left with 4t-12

Answer 20

The - sign goes with the 3 so it is actually
-3(T - 2)

and -3 * -2 = +6

Answer 21

ohhh got it

Answer 22

meeee tooooooo!

Answer 23

YEAH!!!!!

Answer 24

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

Answer 25

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.

Answer 26

noooo wait hold on

Answer 27

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

Answer 28

yes!

Answer 29

OK... First we will simplify the top.

5 x
- - ----
1 x- 1

what is the common denominator?

Answer 30

x-1?

Answer 31

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

Answer 32

5x - 5 x
----- - -----
x - 1 x - 1


4x - 5
------
x - 1



ok?

Answer 33

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

Answer 34

GOT IT

Answer 35

Yes... now add the x's

Answer 36

Now let's do the same to the bottom.

Answer 37

X+2
-----
X+1

Answer 38

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

Answer 39

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

Answer 40

got it

Answer 41

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

Answer 42

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

--------
X+2
---
X+1

Answer 43

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

Answer 44

top right and bottom left cancel out?

Answer 45

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

Answer 46

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

Answer 47

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

????? I HOPE

Answer 48

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

Answer 49

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

Answer 50

(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

Answer 51

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

Answer 52

i got that

Answer 53

Good.

Answer 54

i wanna cry this is hard

Answer 55

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

Answer 56

They are just a lot of steps.

Answer 57

(4x - 7)^2 = -27

Are you sure this is correct?

Answer 58

Yes

Answer 59

yessssssssss

Answer 60

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

Answer 61

yes !

Answer 62

OK.. what if I gave you this problem... do you know what to do.


x^2 = 16

Answer 63

yes square root both sides

Answer 64

Good... so in this problem you have

(something)^2 = -27

so you square root both sides

Answer 65

x=4

Answer 66

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

Answer 67

sqrt(-27) is -3i sqrt(3)

do you understand this?

Answer 68

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

Answer 69

yess!

Answer 70

OOPS you are correct is is positive

Answer 71

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

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

Answer 72

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

Answer 73

wait im not done hold on!

Answer 74

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

Answer 75

simplify and state restricitons

Answer 76

-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?

Answer 77

ok hold on lemme take all that in

Answer 78

then factor?

Answer 79

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)

Answer 80

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

Answer 81

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

Answer 82

now we can cancel out right?

Answer 83

Yes... now cancel anything in ( )'s with like ( )'s

Anything on the top with anything on the bottom that matches.

Answer 84

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

Answer 85

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...

Answer 86

Now you also said you had to tell restrictions.

Answer 87

yesss

Answer 88

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.

Answer 89

We are only concerned with the denominators.

Answer 90

okkk

Answer 91

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

Answer 92

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

Answer 93

And one more you need 0 because of the single x

Every where there is an x there is a restriction.

Answer 94

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

Answer 95

Sure

Answer 96

way better then our professor!

Answer 97

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

SIMPLIFY

Answer 98

Factor