Question

Algebra Question. Finding a common denominator.

Answer 1

Find the Least Common Multiple of the denominators (which is called the Least Common Denominator). Change each fraction (using equivalent fractions) to make their denominators the same as the least common denominator. Then add (or subtract) the fractions, as we wish!"

Answer 2

\[\left(\begin{matrix}m \\ n\end{matrix}\right) +\left(\begin{matrix}m \\ n-1\end{matrix}\right) = \frac{ m! }{ n! (m-n)!}+ \frac{ m! }{ (m-n+1)!(n-1)! }\]

Answer 3

In the next step shown in the answer key the common denominator is shown as \[n!(m-n+1)!\]

I am confused as to how this was obtained.

Answer 4

Im sorry. Im not sure i can help you! Hold on. Ill try to look for something.

Answer 5

thank you!

Answer 6

@SolomonZelman

Answer 7

@pooja195

Answer 8

@jigglypuff314

Answer 9

@Zale101

Answer 10

@AlexandervonHumboldt2

Answer 11

@Owlcoffee
@Agl202
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@G33k
@Gabby_Taylor1224
@Hi-xx
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@jabez177
@Kitten_is_back
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Answer 12

I got nothing, sorry

Answer 13

@LogaNator
@LanHikari22
@LoveDance11
@lolo133t
@MissNoName
@mdjjh16
@nicoleg7
@Owlcoffee
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Answer 14

who add me here

Answer 15

howdy

Answer 16

hi

Answer 17

@RAM231
@Rashadeb1
@SithsAndGiggles
@sleepyjess
@skullpatrol
@Surana
@They_Call_Me_Narii
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Answer 18

That's a lot of people summoned.

Answer 19

I NEED AN ARMY.

Answer 20

dang I don't even know this one srry

Answer 21

Thanks all the same!

Answer 22

I have NO clue. Im sorry

Answer 23

These ones are always confusing to me. Let me see.

Answer 24

I'm wondering if the answer key is wrong. I've heard Lang's Basic Mathematics has some typos.

Answer 25

why am i here

Answer 26

Were the explanation marks meant to be 1's instead? Because if those were actually 1's instead of explanation marks, then my guess is that the n in the whole N(M - N) thing got multiplied, making it the (m - n + 1) answer.

If it was meant to be explanation marks, then I'm at a loss here.

Answer 27

Yep, those are exclamation marks. Factorials.

Answer 28

Now I'm at a loss. Sorry. I think that @misty1212 could help, if she was online.

Answer 29

Thank you.

Answer 30

You're welcome.

Answer 31

it might help to partially expand things out

n! = n*(n-1)!
(m-n+1)! = (m-n+1)*(m-n+1-1)! = (m-n+1)*(m-n)!

Answer 32

YES!

THANK YOU SO MUCH!!!

It's painfully obvious in light of what you have said, but I never would have thought to have looked at simplifying them by partially expanding them.

I really thought I wasn't going to be able to figure it out.

Thank you! Thank you!!!

Answer 33

you're welcome

Answer 34

Nicely done.