Question

Can someone please help me with this math question?
Please? I will fan and give a medal!!

Answer 1

Please help me to simplify this rational expression -
(4x^2-6x-18) (x^2+1)
------------ * -----------
(x+1) (x^2-6x+9)

Answer 2

Have you tried factoring the quadratics ?

Answer 3

Umm I've tried to factor it, but I got stuck at a step, would you like to see the steps I did?

Answer 4

Sure..

Answer 5

@ganeshie8 I was told to mutiply first -
(4x^2−6x−18)(x^2+1)
---------------------
(x-1)(x^2-6x+9)

Answer 6

Looks good
Next try factoring the quadratics

Answer 7

See that is where she left me... We were doing this thing called "box method"

Answer 8

(4x^2-6x-18) = 2(2x^2 - 3x - 9)

Answer 9

Pick two numbers that addup to -3 and multiply to -18

Answer 10

-14+11=-3

Answer 11

Do they multiply to -18 too ?

Answer 12

No sir/ma'am

Answer 13

So -14 and 11 don't work
Pick some other numbers

Answer 14

Give me another minute, I'm not very good with negative numbers

Answer 15

Take your time
This is your chance to master them

Answer 16

Ok so -6 and 3
-6+3=-3
-6*3=18

Answer 17

Perfect!
so -6 and 3 are your magic numbers

Answer 18

(4x^2-6x-18) = 2(2x^2 `- 3x` - 9)


split the middle term `-3x` as `-6x + 3x`

Answer 19

(4x^2-6x-18) = 2(2x^2 `- 3x` - 9)
= 2(2x^2 `- 6x + 3x` - 9)

Answer 20

Convince yourself that they both are same

Answer 21

Next, group first two terms and last two terms :

(4x^2-6x-18) = 2[2x^2 `- 3x` - 9]
= 2[2x^2 `- 6x + 3x` - 9]
= 2[(2x^2 `- 6x`) + ( `3x` - 9)]

Answer 22

Now factor out the GCF from each group :

(4x^2-6x-18) = 2[2x^2 `- 3x` - 9]
= 2[2x^2 `- 6x + 3x` - 9]
= 2[(2x^2 `- 6x`) + ( `3x` - 9)]
= 2[2x(x - 3) + 3( x - 3)]

Answer 23

Lastly factor the common x-3 :


(4x^2-6x-18) = 2[2x^2 `- 3x` - 9]
= 2[2x^2 `- 6x + 3x` - 9]
= 2[(2x^2 `- 6x`) + ( `3x` - 9)]
= 2[2x(x - 3) + 3( x - 3)]
= 2[(x - 3)(2x + 3)]

Answer 24

Still wid me ?

Answer 25

Yes sir/ma'am

Answer 26

(4x^2−6x−18)(x^2+1)
---------------------
(x-1)(x^2-6x+9)

Answer 27

plugin the factored form for the top quadratic

Answer 28

(4x^2−6x−18)(x^2+1)
---------------------
(x-1)(x^2-6x+9)


is same as

2(x - 3)(2x + 3)(x^2+1)
---------------------
(x-1)(x^2-6x+9)

Answer 29

see if you can factor the bottom (x^2-6x+9) similarly

Answer 30

pick two numbers that add up to -6 and multiply to +9

Answer 31

@ganeshie8 I can't figure this one out

Answer 32

How about -3 and -3 ?

Answer 33

x^2 - 6x + 9 = x^2 - 3x - 3x + 9
= ?

Answer 34

Oh they can be the same number?!

Answer 35

x^2-3-3+9=4

Answer 36

@ganeshie8

Answer 37

No. You cannot add apples and oranges

Answer 38

Don't neglect x

Answer 39

The idea here is to group and factor

Answer 40

x^2 - 6x + 9
= x^2 - 3x - 3x + 9


group first two terms and last two terms :

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

Answer 41

whats the GCF in first group ?

Answer 42

1? I'm not sure