Question

Prove that the fraction `(21n+4)/(14n+3)` is irreducible for every `n in NN`?

Answer 1

Calculate the GCF of `21n+4` and `14n+3`, finding that it is `1`

Explanation:

Calculate the GCF of `21n+4` and `14n+3`:

`(21n+4)/(14n+3) = 1" "` with remainder `7n+1`

`(14n+3)/(7n+1) = 2" "` with remainder `1`

`(7n+1)/1 = 7n+1" "` with remainder `0`

So the GCF is `1`