To simplify the expression (x+y/x)^3, we can start by expanding it using the binomial theorem.

The binomial theorem states that for any real numbers a and b, and any positive integer n, the expansion of (a+b)^n can be written as:

(a+b)^n = C(n,0) * a^n * b^0 + C(n,1) * a^(n-1) * b^1 + C(n,2) * a^(n-2) * b^2 + ... + C(n,n-1) * a^1 * b^(n-1) + C(n,n) * a^0 * b^n

where C(n,k) is the binomial coefficient, given by C(n,k) = n! / (k! * (n-k)!).

In our case, a = x, b = y/x, and n = 3. Let's expand it:

(x+y/x)^3 = C(3,0) * x^3 * (y/x)^0 + C(3,1) * x^2 * (y/x)^1 + C(3,2) * x^1 * (y/x)^2 + C(3,3) * x^0 * (y/x)^3

= 1 * x^3 * 1 + 3 * x^2 * (y/x) + 3 * x^1 * (y/x)^2 + 1 * x^0 * (y/x)^3

= x^3 + 3xy + 3y^2/x + y^3/x^3

So, the simplified expression is x^3 + 3xy + 3y^2/x + y^3/x^3.