Add or subtract, as indicated. See Example 4. (3/2k) + (5/3k)

Verified step by step guidance

1. Identify the given expression: \(\frac{3}{2k} + \frac{5}{3k}\).
2. Since the denominators are different, find the least common denominator (LCD). Here, the denominators are \$2k\( and \)3k\(. The LCD is \)6k\( because \(6\) is the least common multiple of \(2\) and \(3\), and \)k$ is common in both.
3. Rewrite each fraction with the LCD as the new denominator by multiplying numerator and denominator appropriately: - For \(\frac{3}{2k}\), multiply numerator and denominator by \(3\) to get \(\frac{3 \times 3}{2k \times 3} = \frac{9}{6k}\). - For \(\frac{5}{3k}\), multiply numerator and denominator by \(2\) to get \(\frac{5 \times 2}{3k \times 2} = \frac{10}{6k}\).
4. Now that both fractions have the same denominator, add the numerators: \(\frac{9}{6k} + \frac{10}{6k} = \frac{9 + 10}{6k} = \frac{19}{6k}\).
5. Express the final answer as a single simplified fraction: \(\frac{19}{6k}\). This is the sum of the original expression.

Key Concepts

Adding and Subtracting Algebraic Fractions

To add or subtract algebraic fractions, first find a common denominator. This involves identifying the least common multiple (LCM) of the denominators, then rewriting each fraction with this common denominator before performing the addition or subtraction of the numerators.

Least Common Denominator (LCD)

The least common denominator is the smallest expression that both denominators divide into evenly. For algebraic expressions, this includes factoring variables and constants to find the LCM, ensuring the fractions can be combined correctly.

Simplifying Algebraic Expressions

After combining fractions, simplify the resulting expression by factoring and reducing common terms in the numerator and denominator. This step ensures the final answer is in its simplest form, making it easier to interpret or use in further calculations.