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Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. R - Review of Basic ConceptsProblem 9a
Chapter 1, Problem 9a

Perform the indicated operation, and write each answer in lowest terms. 2x/5 + x/4

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Identify the denominators in the expression: 5 and 4.
Find the least common denominator (LCD) of 5 and 4, which is the smallest number divisible by both denominators.
Rewrite each fraction with the LCD as the new denominator by multiplying numerator and denominator appropriately: for \(\frac{2x}{5}\) multiply numerator and denominator by 4, and for \(\frac{x}{4}\) multiply numerator and denominator by 5.
Add the two fractions by combining their numerators over the common denominator: \(\frac{2x \times 4}{20} + \frac{x \times 5}{20} = \frac{8x + 5x}{20}\).
Combine like terms in the numerator and simplify the fraction if possible by factoring and reducing to lowest terms.

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Key Concepts

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

Adding Rational Expressions

Adding rational expressions involves combining fractions that contain variables. To add them, the denominators must be the same, so you find a common denominator before combining the numerators.
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Rationalizing Denominators

Finding the Least Common Denominator (LCD)

The least common denominator is the smallest expression that both denominators divide into evenly. For numerical denominators like 5 and 4, the LCD is their least common multiple, which is essential for rewriting fractions with a common denominator.
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Rationalizing Denominators Using Conjugates

Simplifying Fractions

After performing operations on fractions, simplifying means reducing the fraction to its lowest terms by dividing numerator and denominator by their greatest common factor. This makes the expression easier to interpret and use.
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Radical Expressions with Fractions
Related Practice
Textbook Question

Work each problem. Which of the following is the correct complete factorization of x4−1x^4-1?

A. (x2−1)(x2+1)(x^2-1)(x^2+1)

B. (x2+1)(x+1)(x−1)(x^2+1)(x+1)(x-1)

C. (x2−1)2(x^2-1)^2

D. (x−1)2(x+1)2(x-1)^2(x+1)^2

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Perform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. (2 + √3) (2 - √3)

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Evaluate each expression. |-4|

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Textbook Question

Work each problem. Which of the following is the correct factorization of x3+8?

A. (x+2)3

B. (x+2)(x2+2x+4)

C. (x+2)(x2-2x+4)

D. (x+2)(x2-4x+4)

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Textbook Question

Match each expression in Column I with its equivalent expression in Column II. Choices may be used once, more than once, or not at all.

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