/*! 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 23 Reduce each rational expression ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 23

Reduce each rational expression to its lowest terms. $$\frac{2 x+2}{4}$$

Short Answer

Expert verified
\( \frac{x+1}{2} \)

Step by step solution

01

Factor the Numerator

Look at the numerator of the given rational expression \(2x+2\). Factor out the common factor which is 2. \[\frac{2(x+1)}{4}\]
02

Simplify the Fraction

Next, observe that both the numerator and the denominator share a common factor of 2. Simplify the fraction by dividing both the numerator and the denominator by this common factor. \[\frac{2(x+1)}{4} = \frac{x+1}{2}\]

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.

factoring
Factoring is the process of breaking down a complex expression into simpler factors that, when multiplied together, give you the original expression. It makes working with the expression easier, especially when you're simplifying rational expressions.
In our exercise, we started with the numerator of the rational expression, which is 2x + 2. By factoring, we find a common factor of 2. Factoring it out, the numerator becomes 2(x + 1).
Think of it like finding the building blocks of an expression. For example, in 6x, the factors are 2, 3, and x. Understanding factoring helps simplify the steps you need to reduce an expression.
common factors
Common factors are those numbers or expressions that two or more numbers share in common. In the context of rational expressions, finding common factors helps in simplifying them.
Looking at our problem, the numerator after factoring was 2(x+1). We also had 4 in the denominator. The common factor between the numerator and the denominator is 2. By recognizing that both the numerator and the denominator can be divided by the same common factor, we simplify the fraction more easily.
It's like reducing fractions in arithmetic. For example, in the fraction 8/12, the common factor is 4, so simplifying by dividing both by 4 gives you 2/3.
simplifying fractions
Simplifying fractions involves reducing them to their lowest terms, so they are easier to work with and understand.
For our rational expression \(\frac{2x+2}{4}\), we first factored it to get \(\frac{2(x+1)}{4}\). We then found the common factor of 2. By dividing both the numerator and the denominator by this common factor, we reduced the expression to its simplest form: \(\frac{x+1}{2}\).
This process is crucial for solving and understanding algebraic problems because it allows you to work with simpler expressions. Simplified fractions are easier to interpret and calculate with, which is helpful in more complex problems.

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

Perform the indicated operations. When possible write down only the answer. $$\frac{-1}{x-1} \cdot \frac{1-x}{2}$$

Find the solution set to each equation. $$\frac{x-2}{x-3}=\frac{x+5}{x+2}$$

Writing. In this chapter the LCD is used to add rational expressions and to solve equations. Explain the difference between using the LCD to solve the equation $$\frac{3}{x-2}+\frac{7}{x+2}=2$$ and using the LCD to find the sum $$\frac{3}{x-2}+\frac{7}{x+2}$$

Solve each equation. Identify each equation as a conditional equation, an inconsistent equation, or an identity. State the solution sets to the identities using interval notation. $$\frac{1}{x}+\frac{1}{2 x}=\frac{3}{2 x}$$

Perform the indicated operations. $$\frac{2 x^{2}+7 x-15}{4 x^{2}-100} \cdot \frac{2 x^{2}-9 x-5}{4 x^{2}-1}$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

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.