Add or subtract, as indicated. 3/2k + 5/3k

Verified step by step guidance

1. Identify the like terms in the expression. Here, both terms have the variable \(k\), so they can be combined.
2. Find the least common denominator (LCD) of the fractions \(\frac{3}{2}\) and \(\frac{5}{3}\). The denominators are 2 and 3, so the LCD is 6.
3. Rewrite each fraction with the denominator 6: multiply numerator and denominator of \(\frac{3}{2}\) by 3 to get \(\frac{9}{6}\), and multiply numerator and denominator of \(\frac{5}{3}\) by 2 to get \(\frac{10}{6}\).
4. Add the fractions: \(\frac{9}{6}k + \frac{10}{6}k = \frac{9 + 10}{6}k = \frac{19}{6}k\).
5. Write the final expression as a single term: \(\frac{19}{6}k\).

Key Concepts

Like Terms

Like terms are terms that have the same variable raised to the same power. In this problem, both terms contain the variable 'k', so they can be combined by adding or subtracting their coefficients.

Adding and Subtracting Fractions

To add or subtract fractions, they must have a common denominator. Find the least common denominator (LCD) of the fractions, convert each fraction to an equivalent fraction with the LCD, then add or subtract the numerators.

Simplifying Algebraic Expressions

After combining like terms and performing fraction operations, simplify the expression by reducing fractions to their simplest form and combining coefficients to write the final answer clearly.