Solve the Equation: 1/x + x² = 9/x in Rational Form

$\frac{1}{x}+x^2=\frac{9}{x}$

To solve the equation $\frac{1}{x} + x^2 = \frac{9}{x}$, we follow these steps:

• Step 1: Eliminate the fractions by multiplying both sides of the equation by $x$, yielding $1 + x^3 = 9$.
• Step 2: Rearrange the equation to standard form: $x^3 + 1 = 9$. Simplify this to $x^3 = 8$.
• Step 3: Solve for $x$ by taking the cube root of both sides: $x = \sqrt[3]{8}$ or simply $x = 2$.

Thus, the solution to the equation $\frac{1}{x} + x^2 = \frac{9}{x}$ is $x = 2$.