Question

some one please teach me how to do these please? im so confused :c

simplify the expression x^2 + 6x + 9 / 5x + 15

Answer 1

x^2 + 6x + 9 do you know how to factor this?

Answer 2

factoring means rewriting so it is 2 things mulitplied together

( ) ( ) what times what = x^2

Answer 3

i have no clue...

Answer 4

(x + 3 )(x + 3) = x^2 + 6x + 9
------------ ------------
5x + 15 do you know the commond denominator

Answer 5

what divides evenly into both 5 and 15

Answer 6

3

Answer 7

wait how did you get that equation?!?!

Answer 8

which one?

Answer 9

(x + 3 )(x + 3) = x^2 + 6x + 9
------------ ------------
5x + 15

Answer 10

x^2 + 6x + 9 if we factor it, it will be (x + 3)(x + 3)

try it, do you know how to multiply (x+ 3)(x + 3)

Answer 11

um 3x and 3x? im sorry im so confused

Answer 12

ok lets start from the begining.

(x + 3)(x+ 3) have your heard of FOIL?

Answer 13

ive heard of it.. but i dont how to use it

Answer 14

It tells us how to multiply to binomials

(x + 3) (x + 3 )
F irst O uter I nner L asts
x *x x * 3 3 * x 3 * 3 do you see where I got this?

Answer 15

Ohhh i see! but i still dont get who you got the 3.. do you use 3 in every expression like this one?

Answer 16

how not who **

Answer 17

ok just lets finish this

F irst O uter I nner L asts
x *x x * 3 3 * x 3 * 3
x^2 + 3x + 3x + 9
x^2 + 6x + 9

Answer 18

x^2 + 6x + 9
now ,do you see how this is in your original problem?

Answer 19

OHHHH yes! thank you! okay go on :)

Answer 20

oh wait you factor the numberator

Answer 21

okay i got that part and then you factor the denominator which is....?

Answer 22

x^2 + 6x + 9
to factor this, I start off with what time what = x^2

x * x = x^2 , so I put it in the front

(x )(x )

Answer 23

x time x = x^2

Answer 24

x * 3 and x* 3 ??

Answer 25

(x + 3)(x +3)

Answer 26

right right. sorry... go on! :)

Answer 27

now look at the denominator 5x + 15

what number divides evenly into both 5 and 15
(it is not 3)

Answer 28

5 !

Answer 29

right, that is the common denominator....

Answer 30

so the factors are ( x + 5) and ( x +5 ) ??

Answer 31

or just ( x + 3 ) ( x + 3 )
---------------
5

Answer 32

this one is a little different...

5x + 15 common denominator is 5

5( ) now divide everthing by 5

Answer 33

5x + 15 common denominator is 5
--- ---
5 5

5( x + 3) now divide everthing by 5

Answer 34

(x + 3 )(x + 3) = x^2 + 6x + 9
------------ ------------
5 (x + 3) 5x + 15

Answer 35

what can You cancel out?

Answer 36

the threes !

Answer 37

the (x +3)s

Answer 38

yes

Answer 39

leaving you with x + 3
------
5

Answer 40

thats the answer??

Answer 41

you only can cancel one out so the other is left

Answer 42

yet that is the answer

Answer 43

* yep

Answer 44

Ohhh i get it thank you sooooooo much! heres your medal :D

Answer 45

yw

Answer 46

can you help me with another one? i just need help going through it...

Answer 47

sure...

Answer 48

okay its \[2x^2 - 4a +2 / 3a^2 - 3\]

Answer 49

so i factor the numberator which is... (x-2) (x+2) ??

Answer 50

yes you have to factor the numerator...but start by looking for a GCF

What divides evenly into 2, -4 and 2

Answer 51

its -2 or 2

Answer 52

yes, usually we will keep it positive, so lets use 2

2a^2 -4a + 2
--- --- ---
2 2 2

2 (

Answer 53

what is 2a^2 divided by 2

Answer 54

a^2 ??

Answer 55

\[\frac{ 2a^2 }{ 2 }\]

Answer 56

a squared

Answer 57

right, divide each of the terms by 2

Answer 58

2a^2 -4a + 2

2 (a^2 - 2a + 1) do you see where I got that?

Answer 59

so its a^2 - 2a +1

Answer 60

yes you divided 2 to every thing

Answer 61

by everything i mean the numberator numbers

Answer 62

ok now we have to factor that

2 (a^2 -2a + 1 )

2 (a )(a ) what 2 numbers mult to get 1 and add to get -2?

Answer 63

-1 and -1

Answer 64

right that is what you put in the parentheses

2 (a - 1 )(a - 1 ) now that is factored

Answer 65

ok

Answer 66

now factor 3a^2 -3 what is the GCF?

Answer 67

what goes evenly into 3 and -3?

Answer 68

1?

Answer 69

yes 1 does, but is it the biggest that goes evenly into both?

Answer 70

3 !!!! duhh!! haha oops!

Answer 71

right now divide everything by 3
3a^2 -3
-- --
3 3

3 (

Answer 72

all thats left is a^2

Answer 73

a^2 -1

Answer 74

right...
3 (a^2 - 1) this can still be factored though...

Answer 75

3 (a )( a )

Answer 76

what 2 numbers can you mult together to get -1

Answer 77

3 (a-1) ( a-1) ??

Answer 78

almost... -1* -1 = 1

Answer 79

ohh ok i get i

Answer 80

so its 3 (a +1) (a + 1)

Answer 81

almost again -1 * +1 = -1

2 (a - 1 )(a - 1 )
---------------------- which cancels out?
3 (a +1) (a - 1)

Answer 82

the ones cancel out so its just 2/3

Answer 83

right?

Answer 84

anything divided by itself equal 1

(a-1)/(a-1) = 1

one (a -1) on top and one (a-1) on bottom cancels, whats left?

Answer 85

2(a-1)
------
3 (a+1)

Answer 86

thats right, thats the answer...

Answer 87

THANKYOU so much for your help! im not going to fail! :D haha

Answer 88

keep working at it, youll get it!

Answer 89

thanks!