Add or subtract, as indicated. (17y + 3)/(9y + 7) - (-10y - 18)/(9y + 7)

Verified step by step guidance

1. Identify the common denominator in both fractions, which is $9y+7$.
2. Since the denominators are the same, you can combine the numerators by subtraction: $(17y+3)-(-10y-18)$.
3. Distribute the negative sign across the second numerator: $17y+3+10y+18$.
4. Combine like terms in the numerator: $(17y+10y)+(3+18)$.
5. Simplify the expression to get the final numerator over the common denominator $9y+7$.

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, both expressions share a common denominator, which simplifies the process of combining them.

Common Denominator

A common denominator is a shared multiple of the denominators of two or more fractions. When adding or subtracting rational expressions, having a common denominator allows for straightforward combination of the numerators. In the given question, both fractions have the same denominator (9y + 7), facilitating the operation.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This concept is essential when simplifying the result after performing operations on rational expressions. In the context of the question, after finding a common denominator, the numerators can be combined by adding or subtracting their coefficients.