Add or subtract, as indicated. See Example 4. 1 b—— + —— a a²

Verified step by step guidance

1. Identify the common denominator for the fractions \( \frac{1}{a} \) and \( \frac{b}{a^2} \). The common denominator is \( a^2 \).
2. Rewrite the first fraction \( \frac{1}{a} \) with the common denominator \( a^2 \). Multiply the numerator and the denominator by \( a \) to get \( \frac{a}{a^2} \).
3. The second fraction \( \frac{b}{a^2} \) already has the common denominator \( a^2 \), so it remains unchanged.
4. Add the two fractions: \( \frac{a}{a^2} + \frac{b}{a^2} \).
5. Combine the numerators over the common denominator: \( \frac{a + b}{a^2} \).

Key Concepts

Common Denominator

In order to add or subtract fractions, they must have a common denominator. The common denominator is a shared multiple of the denominators of the fractions involved. For example, in the expression 1/a + 1/a², the common denominator would be a², allowing the fractions to be combined into a single fraction.

Fraction Addition/Subtraction

Adding or subtracting fractions involves combining the numerators while keeping the common denominator. For instance, when adding 1/a and 1/a², you would convert both fractions to have the same denominator, then add the numerators together. This process simplifies the operation and allows for a clearer result.

Simplification of Fractions

After performing operations on fractions, it is often necessary to simplify the result. Simplification involves reducing the fraction to its lowest terms by dividing the numerator and denominator by their greatest common divisor (GCD). This step ensures that the final answer is presented in the simplest form, making it easier to understand and use.