https://file.aiquickdraw.com/mathbot/file/1727208444567cft1zyt2.jpg

The equation from the image is:

\[
\frac{x + 1}{2} + \frac{3}{x} = 3
\]

Let's solve it step by step.

1. Multiply every term by the least common denominator (LCD), which is \(2x\), to eliminate the fractions:

\[
2x \left(\frac{x + 1}{2}\right) + 2x \left(\frac{3}{x}\right) = 2x(3)
\]

2. Simplify the equation:

\[
x(x + 1) + 6 = 6x
\]

This expands to:

\[
x^2 + x + 6 = 6x
\]

3. Rearrange all terms to one side:

\[
x^2 + x - 6x + 6 = 0
\]

\[
x^2 - 5x + 6 = 0
\]

4. Now, solve this quadratic equation using factorization:

\[
(x - 2)(x - 3) = 0
\]

Thus, the solutions are:

\[
x = 2 \quad \text{or} \quad x = 3
\]

The solutions to the equation are \(x = 2\) and \(x = 3\).

Would you like a detailed explanation of any step, or do you have any questions?

### Related Questions
1. How do you check if both solutions are valid for the original equation?
2. How can you solve quadratic equations using the quadratic formula?
3. What other methods can you use to solve linear equations with fractions?
4. How does multiplying by the LCD help in solving equations with fractions?
5. How can you verify the factorization of a quadratic equation?

### Tip
Always check your solutions by substituting them back into the original equation, especially when dealing with fractions or possible restrictions (like \(x \neq 0\) here).

Learn how to solve the equation (x + 1) / 2 + 3 / x = 3 by eliminating fractions, leading to a quadratic equation. This problem is ideal for students in Grades 7-9 and covers algebraic concepts including fractions, quadratic equations, and factorization.

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