Domanda del libro di testo
Add or subtract, as indicated. See Example 6. 5√3 + √12
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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 91
Simplify each complex fraction. See Examples 5 and 6. [(y + 3)/y − 4/(y − 1)] / [(y/y + 1/y) / (y − 1) + 1/y]
Guida verificata passo dopo passo1
Rewrite the complex fraction clearly by expressing the numerator and denominator separately. The numerator is \(\frac{y + 3}{y} - \frac{4}{y - 1}\) and the denominator is \(\frac{y}{y - 1} + \frac{1}{y}\).
Find a common denominator for the terms in the numerator. The denominators are \(y\) and \(y - 1\), so the common denominator is \(y(y - 1)\). Rewrite each fraction with this common denominator.
Combine the fractions in the numerator by subtracting the numerators over the common denominator \(y(y - 1)\).
Similarly, find a common denominator for the terms in the denominator, which are \(y - 1\) and \(y\). The common denominator is also \(y(y - 1)\). Rewrite and add the fractions in the denominator.
Now, rewrite the entire complex fraction as a division of two fractions with the same denominator \(y(y - 1)\). When dividing, multiply the numerator fraction by the reciprocal of the denominator fraction, then simplify the resulting expression by canceling common factors.
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Complex Fractions
A complex fraction is a fraction where the numerator, denominator, or both contain fractions themselves. Simplifying involves rewriting the expression as a single fraction by finding common denominators or multiplying numerator and denominator by the least common denominator (LCD) to eliminate the smaller fractions.
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Percorso guidato
4:22
Dividing Complex Numbers
Finding the Least Common Denominator (LCD)
The LCD is the smallest expression that all denominators in a problem divide into evenly. Identifying the LCD allows you to combine or simplify fractions by converting them to equivalent fractions with a common denominator, which is essential for simplifying complex fractions.
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Percorso guidato
3:42Rationalizing Denominators Using Conjugates
Algebraic Manipulation of Rational Expressions
This involves applying algebraic techniques such as factoring, expanding, and canceling common factors in expressions with variables in numerators and denominators. Mastery of these skills is crucial for simplifying complex fractions that contain polynomial expressions.
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Percorso guidato
2:58Rationalizing Denominators
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(Modeling) Distance from the Origin of the Nile River The Nile River in Africa is about 4000 mi long. The Nile begins as an outlet of Lake Victoria at an altitude of 7000 ft above sea level and empties into the Mediterranean Sea at sea level (0 ft). The distance from its origin in thousands of miles is related to its height above sea level in thousands of feet (x) by the following formula.
Distance = (7 − x) / (0.639x + 1.75)
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Domanda del libro di testo
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Domanda del libro di testo
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