• Support PF! Buy your school textbooks, materials and every day products Here!

Canceling a Common Factor

  • Thread starter Drakkith
  • Start date
  • #1
Drakkith
Staff Emeritus
Science Advisor
20,746
4,452

Homework Statement



I've got a fraction here:

[itex]\frac{14+14\sqrt{3}}{-8}[/itex]

Why is it you can take a 2 out of the bottom and top to make it the following?

[itex]\frac{7+7\sqrt{3}}{-4}[/itex]

I'm lost in figuring out how this works. I thought the top was like having (14+14x), where you can take a 14 out of each term and make it 14(1+x).
 

Answers and Replies

  • #2
Mentallic
Homework Helper
3,798
94
What does
[tex]\frac{14y}{2x}[/tex]
equal to?

Also, you can move the negative sign from the denominator to the numerator by "taking out" a -1 from both the numerator and denominator.
 
  • #3
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
12,798
1,666
Really?

Code:
Lookit:
14 + 14*Sqrt(3)      2*7 + 2*7 * Sqrt(3)     2*[7 + 7 * Sqrt (3)]     7 + 7 * Sqrt (3)
---------------- =   ------------------- =   -------------------- = ----------------
     -8                     2*(-4)                   2 * (-4)               -4
 
  • #4
Drakkith
Staff Emeritus
Science Advisor
20,746
4,452
I understand that 14y/2x = 7y/x.

I thought you couldn't divide the original fraction that way because it's still adding up there and you had to take a factor out or something first.
 
  • #5
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
12,798
1,666
Multiplication distributes over addition, so a*(b + d) = a*b + a*d
 
  • #6
Mentallic
Homework Helper
3,798
94
I understand that 14y/2x = 7y/x.

I thought you couldn't divide the original fraction that way because it's still adding up there and you had to take a factor out or something first.
Yes, that's true, but look at what you said earlier

I'm lost in figuring out how this works. I thought the top was like having (14+14x), where you can take a 14 out of each term and make it 14(1+x).
So in this case, the numerator is [itex]14(1+\sqrt{3})[/itex] so we can now let [itex]y=1+\sqrt{3}[/itex].
 
  • #7
Drakkith
Staff Emeritus
Science Advisor
20,746
4,452
So in this case, the numerator is [itex]14(1+\sqrt{3})[/itex] so we can now let [itex]y=1+\sqrt{3}[/itex].
Arrghh... I had my answer as [itex]\frac{7(1+\sqrt{3})}{4}[/itex] , which was apparently wrong, whereas [itex]\frac{7+7\sqrt{3})}{4}[/itex] was correct.
 
  • #8
Office_Shredder
Staff Emeritus
Science Advisor
Gold Member
3,750
99
Arrghh... I had my answer as [itex]\frac{7(1+\sqrt{3})}{4}[/itex] , which was apparently wrong, whereas [itex]\frac{7+7\sqrt{3})}{4}[/itex] was correct.
Those are both the exact same number, and are equally correct actually (well, except for the missing minus sign)
 
  • #9
Drakkith
Staff Emeritus
Science Advisor
20,746
4,452
Those are both the exact same number, and are equally correct actually (well, except for the missing minus sign)
Ah yes, forgot the negative.
At least I got it figured out. I was so confused...
 

Related Threads on Canceling a Common Factor

  • Last Post
Replies
4
Views
2K
Replies
2
Views
3K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
3
Views
1K
Replies
4
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
2
Views
934
  • Last Post
Replies
22
Views
9K
Top