Q.

Find the largest integral value of x such that \(\large \frac{x+6}{x-6}\) is a positive integer.

TITA type i.e. Type In The Answer type

18

\(\frac{x+6}{x-6}\) = integer

\(\Rightarrow \frac{x-6+12}{x-6}\) = integer

\(\Rightarrow 1+\frac{12}{x-6}\) = integer

So, (x – 6) is a factor of 12

x – 6 = 1, 2, 3, 4, 6, 12

Largest possibility of x = 12 + 6 = 18