Prove that the fraction $\frac{21 n + 4}{14 n + 3}$ $(21n+4)/(14n+3)$ is irreducible for every $n in NN$ ?

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Answer 1 · 2016-11-10T07:29:51

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

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 $1$

Prove that the fraction (21n+4)/(14n+3)21n+414n+3(21n+4)/(14n+3) is irreducible for every n in NNn in NN?