Add or subtract, as indicated. 5/12x2y - 11/6xy

Ch. R - Review of Basic Concepts

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Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 57a

Chapter 1, Problem 57a

Add or subtract, as indicated. 5/12x²y - 11/6xy

Verified step by step guidance

Identify the terms given: \(\frac{5}{12}x^2y\) and \(\frac{11}{6}xy\). Notice that these are algebraic terms with variables and coefficients (fractions).

Check if the terms are like terms. Like terms must have the exact same variables raised to the same powers. Here, the first term has \(x^2y\) and the second term has \(xy\). Since the powers of \(x\) differ, these are not like terms.

Since the terms are not like terms, they cannot be combined by addition or subtraction. The expression remains as the sum or difference of the two terms.

Write the expression as it is, keeping the subtraction sign: \(\frac{5}{12}x^2y - \frac{11}{6}xy\).

If needed, you can factor out the common factors from the terms, such as \(xy\), to express the expression in a factored form, but the terms themselves cannot be combined further.

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Key Concepts

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

Like Terms

Like terms are terms that have the exact same variables raised to the same powers. In this expression, terms must have identical variable parts (both in variables and exponents) to be combined through addition or subtraction.

Fraction Operations

When adding or subtracting fractions, you must have a common denominator. This involves finding the least common denominator (LCD) and rewriting each fraction accordingly before performing the addition or subtraction.

Combining Algebraic Expressions

Combining algebraic expressions involves adding or subtracting coefficients of like terms while keeping the variable part unchanged. This simplifies the expression into a more compact form.

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