Is (ab = ac) = (b = c) for all values a?

[CuriousBanker]

I know that by definition, a/(b/c)= a x 1(b/c)...but from there I am lost. Help please!

 

[Travis_King]

Well, I'm terrible at formal proofs, but consider:

a/(b/c)

multiply numerator and denominator by c, so that we get b by itself as the denominator (nobody likes pesky fractions in their denominator):

(c/c)*[a*(b/c)]

You can do this because c/c = 1.

now you have:

(c*a) / [c*(b/c)]

which equals:

(c*a) / b

 

[CuriousBanker]

Nevermind I got it!

 

[CuriousBanker]

Ah, king you posted that just as I got it. Thanks though!

 

[CKH]

a/(b/c) = ac/b

Just a note that you have to be careful. The above is only true when both b and c are not 0. The reason is that division by 0 is undefined. In the above proof (c/c) is used which is 0/0 when c=0. 0/0 is undefined.

I just got shut out of physics thread by a Mentor poster who believed that:

ab = ac implies b = c for all values a. That is not correct when a is 0.