Add or subtract, as indicated. 1/a + b/a²

Verified step by step guidance

1. Identify the terms to be added: \(\frac{1}{a}\) and \(\frac{b}{a^2}\).
2. Find a common denominator for the fractions. Since the denominators are \(a\) and \(a^2\), the least common denominator (LCD) is \(a^2\).
3. Rewrite each fraction with the common denominator \(a^2\): multiply the numerator and denominator of \(\frac{1}{a}\) by \(a\) to get \(\frac{a}{a^2}\), and keep \(\frac{b}{a^2}\) as is.
4. Add the numerators over the common denominator: \(\frac{a}{a^2} + \frac{b}{a^2} = \frac{a + b}{a^2}\).
5. Express the final answer as a single fraction: \(\frac{a + b}{a^2}\).

Key Concepts

Like and Unlike Denominators

When adding or subtracting fractions, the denominators must be the same. Fractions with different denominators are called unlike fractions and require finding a common denominator before performing the operation.

Finding the Least Common Denominator (LCD)

The least common denominator is the smallest expression that both denominators divide into evenly. For algebraic fractions, the LCD is found by factoring denominators and taking the highest powers of each factor.

Adding Fractions with Algebraic Expressions

After rewriting fractions with the LCD, add or subtract the numerators while keeping the common denominator. Simplify the resulting expression by combining like terms and reducing if possible.