Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 59a

Chapter 1, Problem 59a

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

Verified step by step guidance

Identify that both rational expressions have the same denominator, which is \(9y + 7\).

Since the denominators are the same, you can combine the numerators directly by subtracting the second numerator from the first: \((17y + 3) - (-10y - 18)\).

Simplify the expression inside the numerator by distributing the negative sign: \(17y + 3 + 10y + 18\).

Combine like terms in the numerator: \((17y + 10y) + (3 + 18)\).

Write the final expression as a single rational expression with the common denominator: \(\frac{27y + 21}{9y + 7}\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Like Denominators in Rational Expressions

When adding or subtracting rational expressions, having the same denominator allows you to combine the numerators directly. This simplifies the process since you only perform addition or subtraction on the numerators while keeping the denominator unchanged.

Combining Like Terms in the Numerator

After combining the numerators, it is important to simplify by combining like terms—terms that have the same variable raised to the same power. This helps to write the expression in its simplest form and makes further operations easier.

Simplifying Rational Expressions

Once the numerators are combined, the resulting rational expression should be checked for any common factors between numerator and denominator. Factoring and canceling common factors simplifies the expression to its lowest terms.

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