Add or subtract, as indicated. 1/a + b/a^2

Verified step by step guidance

1. Identify the common denominator for the fractions. Here, the common denominator is $a^2$.
2. Rewrite the first fraction $\frac{1}{a}$ with the common denominator $a^2$. Multiply both 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 $a^2$.
4. Now that both fractions have the same denominator, you can add them: $\frac{a}{a^2}+\frac{b}{a^2}$.
5. Combine the numerators over the common denominator: $\frac{a+b}{a^2}$.

Key Concepts

Rational Expressions

Rational expressions are fractions where the numerator and the denominator are polynomials. Understanding how to manipulate these expressions, including addition and subtraction, is crucial for solving problems involving them. In this case, the expression involves terms with a common denominator, which is essential for combining them.

Common Denominator

A common denominator is a shared multiple of the denominators of two or more fractions. To add or subtract rational expressions, it is necessary to express them with a common denominator. In the given expression, the common denominator is a^2, allowing for the combination of the terms effectively.

Combining Fractions

Combining fractions involves adding or subtracting the numerators while keeping the common denominator. This process requires careful attention to the coefficients and variables in the numerators. In the expression 1/a + b/a^2, after finding a common denominator, the terms can be combined to simplify the expression.