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

Verified step by step guidance

1. Identify the problem as an addition of two rational expressions: $\frac{3}{2k}+\frac{5}{3k}$.
2. Find a common denominator for the fractions. The denominators are $2k$ and $3k$, so the least common denominator (LCD) is $6k$.
3. Rewrite each fraction with the common denominator $6k$. Multiply the numerator and denominator of $\frac{3}{2k}$ by 3 to get $\frac{9}{6k}$. Multiply the numerator and denominator of $\frac{5}{3k}$ by 2 to get $\frac{10}{6k}$.
4. Add the two fractions: $\frac{9}{6k}+\frac{10}{6k}=\frac{9+10}{6k}$.
5. Combine the numerators over the common denominator: $\frac{19}{6k}$.

Key Concepts

Like Terms

In algebra, like terms are terms that have the same variable raised to the same power. For example, in the expression 3/2k + 5/3k, both terms involve the variable 'k' and can be combined. Recognizing like terms is essential for simplifying expressions and performing operations such as addition or subtraction.

Finding a Common Denominator

When adding or subtracting fractions, it is necessary to have a common denominator. The common denominator is a shared multiple of the denominators of the fractions involved. In the expression 3/2k + 5/3k, the denominators are 2k and 3k, and the least common denominator would be 6k, which allows for the fractions to be combined correctly.

Simplifying Expressions

Simplifying expressions involves combining like terms and reducing fractions to their simplest form. After finding a common denominator and rewriting the fractions, the next step is to combine the numerators and simplify the resulting expression if possible. This process is crucial for obtaining a clear and concise final answer.