Textbook Question
Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6. ƒ(x + 2)
Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 1, Problem 57
Add or subtract, as indicated. See Example 4. ((17y + 3)/(9y + 7)) - ((-10y - 18)/(9y + 7 ))
Verified step by step guidance1
Identify the expression as a subtraction of two fractions: \(\frac{17y + 3}{9y + 7} - \frac{10y + 18}{9y + 7}\).
Since both fractions have the same denominator \(9y + 7\), you can combine the numerators directly over the common denominator: \(\frac{(17y + 3) - (10y + 18)}{9y + 7}\).
Distribute the subtraction sign across the second numerator: \(\frac{17y + 3 - 10y - 18}{9y + 7}\).
Combine like terms in the numerator: combine \$17y\( and \)-10y\(, and combine \(3\) and \)-18$.
Write the simplified numerator over the denominator \(9y + 7\) to express the final simplified fraction.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Combining Like Terms
Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This simplifies expressions by reducing the number of terms, making it easier to perform further operations such as addition or subtraction of fractions.
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Adding and Subtracting Complex Numbers
Adding and Subtracting Rational Expressions
To add or subtract rational expressions, the denominators must be the same. If they are identical, you combine the numerators directly over the common denominator. This process is similar to adding or subtracting fractions in arithmetic.
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Simplifying Algebraic Expressions
Simplifying algebraic expressions involves reducing the expression to its simplest form by performing operations like combining like terms, factoring, and canceling common factors. This helps in making the expression clearer and easier to interpret or solve.
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Related Practice
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