Explanation Procedure used: Addition or Subtraction of Rational Numbers (Fraction) with unlike denominators: 1. Compute the LCD of the denominators. 2. Write fraction with the LCD as the denominator. 3. Add or subtract the numerators and write the result over the common denominator. 4. Write the result in lowest terms. “ Finding the lowest common denominator ( LCD ) : 1. Find the prime factors of each denominator. 2. For each different prime factor that appears, note the highest power to which it is raised in any one of the denominators. 3. Form the product of all the different prime factors, each raised to the power found in step 2. This product is called the lowest common denominator.” Calculation: The given expression 2 n 2 − n − 4 2 n 2 + 2 n − 4 + 1 n − 1 occurs in optics. Factor the denominators of the above expression as follows. 2 n 2 − n − 4 2 n 2 + 2 n − 4 + 1 n − 1 = 2 n 2 − n − 4 2 n 2 + 4 n − 2 n − 4 + 1 n − 1 = 2 n 2 − n − 4 2 n ( n + 2 ) − 2 ( n + 2 ) + 1 n − 1 = 2 n 2 − n − 4 ( n + 2 ) ( 2 n − 2 ) + 1 n − 1 = 2 n 2 − n − 4 2 ( n + 2 ) ( n − 1 ) + 1 n − 1 Note that, the denominators of the above fractional expression are different. To make the denominators of the fractions equivalent, find the LCD of the denominators. The factors of 2 n 2 + 2 n − 4 are 2 , ( n + 2 ) and ( n − 1 ) . The factor of n − 1 is n − 1 . Thus, the LCD of the denominators of each fractions is the product of 2 , ( n + 2 ) and ( n − 1 ) that is 2 ( n + 2 ) ( n − 1 ) . To make the resulting denominator in each fraction equal to the LCD, multiply and divide the fraction by the proper quantity

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

11th Edition

ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

Publisher: PEARSON+

See similar textbooks

Videos

Question

Chapter 6.6, Problem 63E

To determine

To perform: The indicated operations in the expression 2n2−n−42n2+2n−4+1n−1 and simplify it.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.6, Problem 62E

Chapter 6.6, Problem 64E

Students have asked these similar questions

Problem 3 Ten measurements of an impurity concentration in a process stream have been recorded. The sample mean is 87ppm and the sample standard deviation is ±13 ppm. Consider the null hypothesis that the impurity concentration has a true mean μo. Part A: Desired Probability that the sample mean will satisfy the null hypothesis: P = 0.4 Part B: Using the chart below, determine the4 highest value of the true mean that will lead to the null hypothesis being accepted with the probability assigned in Part A 1.00 0.90 0.80 0.70 0.60 0.50 0.40 Probability of accepting Ho 0.30 0.20 0.10 1 ° 0 30 40 50 75 100 10 0.2 0.4 0.6 0.8 1.0 1.2 =2.5 1.4 1.6 1.8 2.0 2.2 2.4 2.6 d 2.8 3.0 3.2

Problem 2 A chemical reactor system has been designed to perform optimally when operated at 150°C. The hypothesis test that will be used for evaluating the operating temperature will rely on 10 successive temperature measurements and will assign a 95% confidence interval for the result. The reactor system is judged to have a standard deviation of ±3°C. Part A: Actual operating temperature of the process T[°C] = 152.90 Part B: What is the probability that the hypothesis test for operating at 150°C described above will give a false acceptance (i.e., a type II error)?

Problem 1 An airport is served with an average of 10 departures per day to your desired destination. However, all these flights leave at random times. You are trying to decide how long you are willing to wait to catch the next flight after you arrive at airport. Part A: Acceptable waiting time: T [min] = 78min Part B: What is the probability there will be exactly one departure during this waiting time? Part C: What is the probability there will be exactly no departure during this waiting time? Part D: Which calculation (B or C) should you use to make your decision to wait or leave? Why?

Chapter 6 Solutions

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

Ch. 6.1 - Prob. 1PE Ch. 6.1 - Prob. 2PE Ch. 6.1 - Prob. 3PE Ch. 6.1 - Prob. 4PE Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

To perform: The indicated operations in the expression 2 n 2 − n − 4 2 n 2 + 2 n − 4 + 1 n − 1 and simplify it.

Videos

To perform: The indicated operations in the expression 2n2−n−42n2+2n−4+1n−1 and simplify it.

Want to see the full answer?

Chapter 6 Solutions