To solve this equation, we first need to find a common denominator for the fractions.

Recall that a common denominator for fractions is the least common multiple of the denominators. In this case, the denominators are x and x^2 + 1.

The least common multiple of x and x^2 + 1 is x(x^2 + 1), so we will rewrite the fractions with this common denominator:

(x^2 + 1)/x + (x)/(x^2 + 1) = (x(x^2 + 1))/(x(x^2 + 1)) + (x^2)/(x(x^2 + 1))

Now we can combine the fractions with the common denominator:

(x(x^2 + 1) + x^2)/(x(x^2 + 1)) = 2

Now we can simplify the expression:

(x^3 + x + x^2)/(x(x^2 + 1)) = 2

(x^3 + x + x^2)/(x(x^2 + 1)) = 2

(x^3 + x + x^2)/(x^3 + x) = 2

x^3 + x + x^2 = 2(x^3 + x)

x^3 + x + x^2 = 2x^3 + 2x

x^2 - x^3 = x

x(x - 1) = x

Dividing both sides by (x - 1), we get:

x = 1

Therefore, the solution to the equation is x = 1.