Question

Which of the following is not a rational number when n=2?
(a) n/6
(b) (n-2)/7
(c) (n-2)/(n+2)
(d) (n+2)/(n-2)
[abcd are options]
step by step answer

Answer 1

Let see all options where n=2

A)n/6=2/6=1/3 no

B)n-2/7=2-2/7=0/7=0 no

C)(n-2)/(n+2)=2-2/2+2=0/4=0 no

D)(n+2)/(n-2)=2+2/2-2=2/0 infinite

So D) is answer

Answer 2

Option d) (n+2)/(n-2)  is the correct answer.

To Find:

Not a rational number when n =2.

Solution:

Rational numbers are the numbers that be expressed in the form of p/q where q ≠ 0.

(a) n/6

when n= 2

2/6 = 1/3 it is in the form of p/q where q ≠ 0.

∴ n/6 is a rational number at n =2

(b) (n-2)/7

when n=2

(2-2)/7=0/7 it is in the form of p/q where q ≠ 0.

∴ (n-2)/7 is a rational number at n =2

(c) (n-2)/(n+2)

when n=2

(2-2)/(2+2)=0/4 = 0/1 it is in the form of p/q where q ≠ 0.

∴ (n-2)(n+2) is a rational number at n =2

(d) (n+2)/(n-2)

when n=2

(2+2)/(2-2) = 4/0 it is in the form of p/q  but q = 0.

∴(n+2)/(n-2) is not a rational number at n =2

∴  option d) is the correct answer.

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