Question

Prove that the fraction
(21n+4)/(14n+3)
is irreducible for every natural number n.

Answer 1

@mikaela19900630

Answer 2

@qweqwe123123123123111

Answer 3

when does the top equal the bottom?

Answer 4

I am unable to understand your question.

Answer 5

since the top and bottom of the fraction are linear and do not cancel, then we would want to know when the top equal the bottom in order that they could cancel each other out

Answer 6

is it 0 ?

Answer 7

lets try

(21n+4)/(14n+3)

(21(0)+4)/(14(0)+3)

4/3

nope

Answer 8

ok then there is no natural number of such type.

Answer 9

correct, but that is not a "proof"

Answer 10

ok Thankyou sir I got it :)

Answer 11

21n + 4 = 14n + 3

7n = -1

n = -1/7 is the only value of n which would make this reduce to 1. but -1/7 is not a natural number

Answer 12

ok

Answer 13

Thanks Again MOD

Answer 14

21n + 4 = (14n + 3)k
show that 'k' is not natural number,

Answer 15

ok

Answer 16

@experimentX thankyou sir

Answer 17

try making use of induction.

Answer 18

Sure sir

Answer 19

oh yeah I proved it :)