Domanda del libro di testo
Use the graph of y = ƒ(x) to find each function value: (a) ƒ(-2) (b) ƒ(0) (c) ƒ(1) and (d) ƒ(4). See Example 7(d).
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Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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TOC.tableOfContents
- 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
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 1, Problema 67
Add or subtract, as indicated. See Example 4. (3x)/(x² + x − 12) − x/(x² − 16) + x
Guida verificata passo dopo passo1
First, identify the two rational expressions you need to subtract: \(\frac{3x}{x^{2} + x - 12}\) and \(\frac{x}{x^{2} - 16}\).
Next, factor the denominators to find their factored forms: factor \(x^{2} + x - 12\) and \(x^{2} - 16\).
After factoring, determine the least common denominator (LCD) by combining all unique factors from both denominators.
Rewrite each fraction with the LCD as the new denominator by multiplying numerator and denominator by the necessary factors to match the LCD.
Finally, subtract the numerators over the common denominator and simplify the resulting expression if possible.
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Factoring Quadratic Expressions
Factoring involves rewriting quadratic expressions as products of binomials. This is essential for simplifying rational expressions by identifying common factors in numerators and denominators, which helps in performing addition or subtraction of fractions.
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Percorso guidato
6:08
Factoring
Finding a Common Denominator
To add or subtract rational expressions, you must find a common denominator, typically the least common multiple (LCM) of the denominators. This allows the expressions to be combined into a single fraction with a unified denominator.
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Percorso guidato
2:58Rationalizing Denominators
Adding and Subtracting Rational Expressions
Once the denominators are the same, add or subtract the numerators directly while keeping the common denominator. Simplify the resulting expression by combining like terms and factoring if possible.
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Percorso guidato
2:58Rationalizing Denominators
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