Solve the Quadratic Fraction Equation: x^2/9 + 2/9x + 1/9 = 0

Solve the following equation:

$\frac{x^2}{9}+\frac{2}{9}x+\frac{1}{9}=0$

To solve this equation, we shall proceed with these steps:

• Step 1: Clear the fractions. Multiply each term of the equation by 9 to simplify:
• $9 \left(\frac{x^2}{9}\right) + 9 \left(\frac{2}{9}x\right) + 9 \left(\frac{1}{9}\right) = 9 \times 0$
• This simplifies down to $x^2 + 2x + 1 = 0$.
• Step 2: Recognize $x^2 + 2x + 1 = 0$ as a quadratic equation, which can be factored as:
• $(x + 1)^2 = 0$.
• Step 3: Solving $(x + 1)^2 = 0$ gives $x + 1 = 0$, thus $x = -1$.

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

The correct choice that corresponds to this solution from the provided options is $x = -1$.