- #1

karnten07

- 213

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## Homework Statement

Let F be a field. For any a,b [tex]\in[/tex] F, b[tex]\neq[/tex]0, we write a/b for ab^-1. Prove the following statements for any a, a' [tex]\in[/tex]F and b, b' [tex]\in[/tex] F\{0}:

i.) a/b = a'/b' if and only if ab' =a'b

ii.) a/b +a'/b' = (ab'+a'b)/bb'

iii.) (a/b)(a'/b') = aa'/bb'

iv.) (a/b)/a'/b') = ab'/a'b (if in addition a'[tex]\neq[/tex]0)

## Homework Equations

## The Attempt at a Solution

I'm struggling to understand how i am to prove these statements. What am i to take the dashes to mean, because they are often used to show inverses? So for the first one:

a/b=ab^-1 which = a^-1b = a'/b'?