x is rational number (not natural number)then, prove that 15 x is irrational number.

Step 1
Given that x is a rational number but not natural number.
Then x can be expressed as a ratio of an integer to a non-zero integer.
Letx $=p/q$, where p is an negative integer and q is non-zero integer.
Step 2
Now, $15x=15\cdot (p/q)=(15\cdot p)/q=15p/q$
Then, 15x is also a rational number.<br<I think you have made any mistake in your question (15x is not irrational number, but you have wrote 15x is irrational number).