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Ch. R - Algebra Review
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. R - Algebra ReviewProblema 139
Capitolo 1, Problema 139

Simplify. See Example 9. (1/2)/(1 - (√5/2))

Guida verificata passo dopo passo
1
Rewrite the given expression clearly as a fraction: \(\frac{\frac{1}{2}}{1 - \frac{\sqrt{5}}{2}}\).
To simplify the complex fraction, multiply the numerator and denominator by 2 to eliminate the fractions inside the denominator: \(\frac{1}{2} \div \left(1 - \frac{\sqrt{5}}{2}\right) = \frac{1}{2} \times \frac{2}{2 - \sqrt{5}}\).
Simplify the multiplication in the numerator: \(\frac{1}{2} \times 2 = 1\), so the expression becomes \(\frac{1}{2 - \sqrt{5}}\).
Rationalize the denominator by multiplying numerator and denominator by the conjugate of the denominator, which is \(2 + \sqrt{5}\): \(\frac{1}{2 - \sqrt{5}} \times \frac{2 + \sqrt{5}}{2 + \sqrt{5}}\).
Use the difference of squares formula to simplify the denominator: \((2)^2 - (\sqrt{5})^2 = 4 - 5 = -1\). Then write the simplified expression as \(\frac{2 + \sqrt{5}}{-1}\) and simplify the negative sign.

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Rationalizing the Denominator

Rationalizing the denominator involves eliminating any irrational numbers, such as square roots, from the denominator of a fraction. This is typically done by multiplying the numerator and denominator by a conjugate or an appropriate radical to create a rational denominator, simplifying the expression.
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Rationalizing Denominators

Conjugates of Binomials

The conjugate of a binomial expression a + b is a - b, and vice versa. Multiplying a binomial by its conjugate results in the difference of squares, which removes the square root terms and simplifies the expression, a key step in rationalizing denominators.
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Rationalizing Denominators Using Conjugates

Simplifying Radical Expressions

Simplifying radical expressions involves reducing square roots to their simplest form by factoring out perfect squares. This process helps in making expressions easier to work with and is essential when performing operations like addition, subtraction, or rationalization.
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Simplifying Trig Expressions
Pratica correlata
Domanda del libro di testo

For Individual or Group Work (Exercises 147 – 150)In calculus, it is sometimes desirable to rationalize a numerator. To do this, we multiply the numerator and the denominator by the conjugate of the numerator. For example, (6 - √2)/4 = (6 - √2)/4 × (6 + √2)/(6 + √2) = (36 - 2)/(4(6 + √2)) = 34/(4(6 + √2)) = 17/(2(6 + √2)) = 17/(6 + √2).

2√10 + √7 30

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Domanda del libro di testo

Simplify. See Example 9. (-√2/3)/(√7/3)

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Domanda del libro di testo

Simplify. See Example 9. (√7/5)/(√3/10)

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Domanda del libro di testo

For Individual or Group Work (Exercises 147 – 150)In calculus, it is sometimes desirable to rationalize a numerator. To do this, we multiply the numerator and the denominator by the conjugate of the numerator. For example, (6 - √2)/4 = (6 - √2)/4 × (6 + √2)/(6 + √2) = (36 - 2)/(4(6 + √2)) = 34/(4(6 + √2)) = 17/(2(6 + √2)) = 17/(6 + √2). Rationalize each numerator. (6 - √3)/8

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Domanda del libro di testo

Rationalize each denominator. See Example 8. (√2 - √3)/(√6 - √5)

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Domanda del libro di testo

Simplify. See Example 9. (√3/2)/(1 - (√3/2))

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