Question: User: $(x^3+x)/x=2$
1. **State the problem:** Solve the equation $$\frac{x^3 + x}{x} = 2$$ for $x$.
2. **Understand the formula and rules:** When dividing a sum by a term, you can split the division over each term: $$\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}$$, provided $c \neq 0$.
3. **Apply the division:**
$$\frac{x^3}{x} + \frac{x}{x} = 2$$
4. **Simplify each term:**
$$x^{3-1} + 1 = 2$$
$$x^2 + 1 = 2$$
5. **Isolate $x^2$:**
$$x^2 = 2 - 1$$
$$x^2 = 1$$
6. **Solve for $x$ by taking the square root:**
$$x = \pm \sqrt{1}$$
$$x = \pm 1$$
7. **Check for restrictions:** Since the original denominator is $x$, $x \neq 0$ which is satisfied by $x = \pm 1$.
**Final answer:**
$$x = 1 \text{ or } x = -1$$