# Essay on Rational Algebraic Expressions

1019 Words Aug 3rd, 2012 5 Pages
Rational Algebraic Expressions

4. Rational Algebraic Expressions

Note You need to understand how to multiply algebraic expressions using the distributive law before starting work on this tutorial. If you feel you need to review this, go back to 3. Multiplying and Factoring Algebraic Expressions.

Q What is a Rational Expression?

Rational Expression
A rational expression is an algebraic expression of the form P/Q, where P and Q are simpler expressions (usually polynomials), and the denominator Q is not zero.

A rational number is any number that can be written in the form a/b, where a and b are integers and b ≠ 0. it is necessary to exclude 0 because the fraction represents a ÷ b, and division by zero is undefined.

A
Since anything divided by itself is just 1, we can "cancel out" these common factors (that is, we can ignore these forms of 1) to find a simpler form of the fraction:

This process (cancelling first, then multiplying) works with rational expressions, too. * Simplify the following expression:

Simplify by cancelling off duplicate factors:

(If you're not sure how the variable parts were simplified above, you may want to review how to simplify expressions with exponents.)

DIVISION
Dividing Rational Expressions (page 2 of 2)
For dividing rational expressions, you will use the same method as you used for dividing numerical fractions: when dividing by a fraction, you flip-n-multiply. For instance: * Perform the indicated operation:

To simplify this division, I'll convert it to multiplication by flipping what I'm dividing by; that is, I'll switch from dividing by a fraction to multiplying by that fraction's reciprocal. Then I'll simplify as usual:

Can the 2's cancel off from the 20's? No! This is as simplified as the fraction gets.
Division works the same way with rational expressions. * Perform the indicated operation:

To simplify this, first I'll flip-n-multiply. Then, to simplify the multiplication, I'll factor the numerators and denominators, and then cancel any duplicated factors. My work looks like this:

Your

## Related Documents

• ###### Essay Art Is An Expression Of A Community

structures—visual, verbal and vocal—and it is full of content—meaningful. Based on the information from the internet, Martin Heidegger “have interpreted art as the means by which a community develops for itself a medium for self-expression and interpretation.” Art is an expression of a community to show the communication within people, and sometimes it represents how people’s life is. Moreover, art is a powerful voice and emotional idea of what people expect to change. The painting, “Execrable…

Words: 1959 - Pages:
• ###### Essay Rational And Goals Within The Classroom

Rational and Goals Within the same classroom, there are a vast range of diversity in student abilities and needs (CAST, 2011; Rose & Meyer, 2002). It is unfair to simply categorize students into two groups, Regular and Special. Instead, recognizing the fact that each student is a unique individual (Ministerial Council for Education, Early Childhood Development and Youth Affairs, 2008) is significantly critical. The Australian government has been committed to deliver education that is programmed based…

Words: 2043 - Pages:
• ###### Gene Expression Essay

Gene Expression Introduction: Escherichia coli are capable of using lactose as their sole carbon source. E. coli produces the enzyme β-galactosidase to digest the lactose into glucose and galactose. However, it would be inefficient to produce enzymes when there is no lactose available, or if there is a more readily-available energy source available such as glucose. Therefore there must be something controlling the expression of this enzyme. The purpose of the experiment is to determine whether…

Words: 611 - Pages: 3
• ###### Essay Rational Consumer

In economics a rational consumer is defined as the people who act in a rational way and make rational choices, namely spending their money wisely. Utility is a term used to measure the amount of pleasure a consumer gains from a good or service they choose to invest in, thus spending our money wisely, in economic terms is a method of maximizing our own utility. However in today’s world different societies and individuals have failed to distinguish the different between a want and a need, which…

Words: 1026 - Pages: 5
• ###### The Distributive Property of Algebraic Expressions Essay

Distributive property of Algebraic expressions Janet Mency MAT 221 Instructor: Amy Glidewell January 25, 2014 Completing algebra problems can be difficult if you don’t understand the properties of real numbers. There are several properties in algebra dealing with both integers and real numbers; one that will be the focus of this report will be the distributive property. We use this property when we are combining addition and multiplication in an algebraic expression. Let’s say that you are…

Words: 822 - Pages: 4
• ###### Essay The Expression Of Architecture

The Expression of Architecture The language is the capacity of transmit and receive some information and understand this message, giving it a signification. It is the base of all communication and exchange in human being interaction. This pattern is not only speaking or texting, all human act have meaning and can transfer some idea – architecture, by it forms and shapes, can express a lot. After The Second Word War a new aesthetic, called Modernism, made architecture and all society to change its…

Words: 1053 - Pages:
• ###### Essay Freedom Of Expression Like A Shadow

Throughout history censorship has followed people’s freedom of expression like a shadow. When I fled my country Ethiopia, not only as a result of censorship, but also extreme intimidation, I left my entire family behind. While others continued to write controversial statements about the government and politics, I left because I was not a fighter. Even though Ethiopia’s Constitution explicitly protects freedom of speech, in reality the government ignores it for the most part. In 2011, Reeyot Alemu…

Words: 1325 - Pages: 6
• ###### Essay Are People Rational

Everyday people make decisions that affect themselves and other parties. This essay will discuss if people are rational and if people are reasonable. In particular will be focusing on whether people are rational in the economist’s sense, and, reasonable in the lawyer’s sense and whatever the outcome, does it matter? It is an important matter as peoples actions have effects, externalities on others, on third parties and it is significant to understand why people act the way they do and comprehend…

Words: 3375 - Pages: 14
• ###### Essay Rational Organisation

features of rational organisation and what are its strengths and weaknesses? To what extent would you recommend rational organisation design as the way forward for junction hotel? This essay will take an in depth analysis of the rational organisation design and evaluate the affects that it will implement on Junction Hotel, if they decide to run their organisation according to the rational theory. This will entail a detailed look into theorists such as Frederick Taylor who supported the rational approach…

Words: 1811 - Pages: 8
• ###### Essay The Rational Choice Theory Of Crime

income may perhaps allow them to sustain a healthy standard of living. Seldom do individuals who receive a solid income have to resort to the opportunity to commit a crime. The rational choice theory is a great way to identify how and why low income minorities are more likely to commit crimes. “Scholars working within the rational choice theoretical tradition have noted how individual perceptions of the relative costs and benefits of engaging in any particular form of criminal behavior are a consequence…

Words: 1084 - Pages: 5