Add or subtract, as indicated. See Example 4. 17y + 3 -10y - 18 ———— - ————— 9y + 7 9y + 7

Verified step by step guidance

1. Step 1: Recognize that the problem involves subtracting two rational expressions with the same denominator.
2. Step 2: Since the denominators are the same, you can combine the numerators directly. Write the expression as a single fraction: $\frac{(17y+3-10y-18)}{9y+7}$.
3. Step 3: Simplify the numerator by combining like terms. Combine $17y$ and $-10y$, and $3$ and $-18$.
4. Step 4: After simplifying the numerator, you should have a new expression in the form $\frac{(ay+b)}{9y+7}$, where $a$ and $b$ are the simplified coefficients.
5. Step 5: The expression is now simplified. Ensure that the denominator is not zero by checking the value of $y$ that would make $9y+7=0$.

Key Concepts

Algebraic Expressions

Algebraic expressions are mathematical phrases that can include numbers, variables, and operators. In the context of the given question, understanding how to manipulate these expressions—specifically, combining like terms and simplifying—is essential for performing the addition or subtraction indicated.

Rational Expressions

Rational expressions are fractions where the numerator and/or denominator are polynomials. The question involves subtracting two rational expressions, which requires knowledge of how to find a common denominator and combine the fractions correctly to simplify the result.

Simplifying Fractions

Simplifying fractions involves reducing them to their lowest terms by dividing the numerator and denominator by their greatest common factor. In this problem, after performing the addition or subtraction of the rational expressions, it is crucial to simplify the resulting expression to present the final answer in its simplest form.