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Let the number be x.
So x-2 =15/x, or
x^2–2x-15=0, or
(x-5)(x+3)=0
Hence x = 5 or -3.
Check: When x=5, 5–2=3 which is 15/5=3.
When x=-3, -3–2=-5 which is 15/-3=-5.
The number is 5 or -3.