Add the following and simplify the sum if possible.
$\frac{x+1}{3x}+\frac{2x-1}{3x}$

• A. $1$
• B. $-1$
• C. $x$
• D. $-x$

Answer: (A)

Verified step by step guidance

1. Identify that both fractions have the same denominator, which is \$3x$. When adding fractions with the same denominator, you can add the numerators directly and keep the denominator the same.
2. Write the sum of the fractions as a single fraction: \(\frac{(x+1) + (2x - 1)}{3x}\).
3. Combine like terms in the numerator: add \(x\) and \$2x\( to get \)3x\(, and add \)1\( and \)-1\( to get \)0\(, so the numerator simplifies to \)3x$.
4. Rewrite the fraction with the simplified numerator: \(\frac{3x}{3x}\).
5. Recognize that \(\frac{3x}{3x}\) simplifies to \$1\( (as long as \(x \neq 0\)), so the sum of the fractions is \)1$.