/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 56 Write each phrase as an expressi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 56

Write each phrase as an expression. The reciprocal of \(x+1\)

Short Answer

Expert verified
The expression is \(\frac{1}{x+1}\).

Step by step solution

01

Understanding the Term 'Reciprocal'

The reciprocal of a number is obtained by dividing 1 by that number. For example, the reciprocal of \(a\) is \(\frac{1}{a}\). So, in this problem, we need to find the reciprocal of the expression \(x+1\).
02

Writing the Reciprocal as an Expression

Now that we know the reciprocal involves taking \(\frac{1}{\text{the original expression}}\), we apply this to our given expression, \(x+1\). Hence, the reciprocal of \(x+1\) can be written as \(\frac{1}{x+1}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Reciprocal
The concept of the reciprocal is foundational in mathematics and helps us understand fractions and division better. A reciprocal of a number is what you multiply with the original number to get the result of 1. Essentially, it is like flipping a number upside down, in a fraction sense. For example, the reciprocal of 5 is \( \frac{1}{5} \) because \( 5 \times \frac{1}{5} = 1 \). This idea extends to expressions with variables as well.
  • Reciprocals are used to simplify equations and solve for unknowns.
  • Finding a reciprocal involves flipping the numerator and denominator for fractions.
  • The reciprocal of an expression keeps the variable in the denominator after inversion.
Expressions
An expression in algebra represents a combination of numbers, variables, and operations. These can be simple or complex, depending on the number of operations and components involved. Variables like \(x\) create the flexibility in expressions, allowing them to represent different values. Consider the expression \(x+1\):
  • This is a linear expression, containing a variable \(x\) and the constant 1.
  • Expressions allow for a concise way to perform operations and share mathematical relationships.
  • They enable us to substitute variables to evaluate or solve them for a range of values.
When converting expressions to find reciprocals, it鈥檚 crucial to interpret their structure correctly to make the operation valid, like changing \(x+1\) into \(\frac{1}{x+1}\). This transformation is a core part of working with reciprocals in algebra.
Step by Step Solution
Following a step-by-step solution approach aids in breaking down complex problems into manageable parts. Let's understand how it works in the context of finding the reciprocal of \(x+1\).First, comprehend what 'reciprocal' means (as explained earlier). Understanding the term removes confusion about what type of transformation is needed for the expression. Next, move to apply this understanding by literally flipping the expression as a fraction. The step-by-step resolution makes it easier to:
  • Grasp the concept of reciprocals through direct calculation.
  • Ensure each action aligns with mathematical principles, like inverting to convert \(x+1\) into \(\frac{1}{x+1}\).
  • Identify potential errors in calculation and reasoning.
This systematic method is particularly helpful when learning or teaching new algebraic concepts, as it simplifies the complexity into straightforward steps.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Simplify each expression. $$ \frac{2 x^{2}+7 x-4}{x^{2}+3 x-4} $$

Perform the indicated operations. $$ \frac{5 x}{7} \cdot \frac{9 x}{7} $$

To calculate a quarterback's rating in NCAA football, you may use the formula \(\frac{100 C+330 T-200 I+8.4 Y}{A}\), where \(C=\) the number of completed passes, \(A=\) the number of attempted passes, \(T=\) the number of touchdown passes, \(Y=\) the number of yards in the completed passes, and \(I=\) the number of interceptions. Sam Bradford of the University of Oklahoma was selected as the 2008 winner of the Heisman Memorial Trophy as the Most Outstanding Football Player. Bradford, a sophomore quarterback with the Sooners, ended the season with 442 attempts, 302 completions, 4464 yards, 53 touchdowns, and only 6 interceptions. Calculate Bradford's quarterback rating for the 2008 season. (Source: NCAA) Round the answer to the nearest tenth.

Write two rational expressions with the same denominator whose difference is \(\frac{x-7}{x^{2}+1}\).

Which of the following are incorrect and why? $$ \frac{1+2}{1+3} \text { simplifies to } \frac{2}{3} $$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.