Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Watch this step-by-step video, matched to your homework problem.

Try Numerade Free for 30 Days

Like

Report

In $3-20$ , perform the indicated additions or subtractions and write the result in simplest form. In each case, list any values of the variables for which the fractions are not defined.$$3+\frac{2}{x}$$

$\frac{3 x+2}{x}$$x \neq 0$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 4

Adding and Subtracting Rational Expressions

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

Missouri State University

Oregon State University

Harvey Mudd College

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

06:28

In $3-20$ , perform the in…

01:36

04:14

04:40

00:41

01:30

03:30

03:04

03:13

03:49

with this one. I think the first and most important thing is to recognize that one of my terms is expressed is a fraction, and one of them is not one of the easiest ways to accidentally and make a mistake with math problems that we know we're capable of doing is to allow a problem to continue to stay where things were being expressed in different forms, meaning, If I see one terms expresses a fraction, I want my entire equation to be expressed as a fraction. It's not necessarily required, but I do think it helps if you will be able to visualize better. And it's a takes very little time. How do we write? Three is a fraction. Well, any whole number that's not written as a fraction just means need to put it over one. That's all it means. So I'm simply going to rewrite this as 3/1 plus two over X. I recognize we could have easily just kept the memory in our head. That three is really being looked at as 3/1. But why not take the time to go ahead and write that just to not make us have to remember more things than necessary. Writing it this way makes it very obvious to me that we do not have a common denominator. So of course we can't solve out this problem yet until we have successfully got a common denominator. Well, between one and X, I don't think X is going to be able to multiply upto one. That doesn't really make sense. But I do think I could multiply one upto X so I don't have to mess with my second fraction. Aiken, just rewrite that one to over extend, stay two of Rex. But 3/1 needs to be changed. I need to change this into something over X. Remember, the way that works is whatever I multiply my denominator by, I have to multiply my denominator by as well so that I don't change the actual value of the term. Okay, well, we know one times X gives us X or an s pretty straightforward. One times, anything is just itself. So if I'm going to multiply by X and my denominator, though I also have to multiply by X in my numerator three times X would give us three x meaning. Now we have a common denominator that I know. I can express 3/1 as three x over X. So now that we have a common denominator, we can go ahead and add the's. We can combine them. Remember, when we combine fractions, you do not combine denominators. You simply just rewrite it. You Onley, combine the numerator the tops three X plus two. Now I can't actually combine those together because they're not like terms. So the best I can do is say OK, I have three X Plus two as a quantity. That's the best I can do because Three X Plus two is a quantity unless I have exactly the same thing in my denominator of three x plus two, I can't cancel anything, so this would be the answer to this problem. However, we do also need to account for any values that might cause this fraction to become undefined. Meaning. Is there any value for X that would cause us to have zero in the denominator? Well, at any point during the problem, the only thing I ever had was an X in the denominator. So if it's just X, what would you plug in to make X equals zero. Well, that would be zero. So this problem is great. The answer is three X plus two over X. As long as X does not happen to be zero. Because if x happened to be zero, that would cause this problem to be undefined.

View More Answers From This Book

Find Another Textbook

In mathematics, the absolute value or modulus |x| of a real number x is its …

In $3-20$ , perform the indicated additions or subtractions and write the re…

00:35

In $3-38$ write each expression in simplest form. Variables in the radicand …

01:55

For what values of $a$ is $\left(1-\frac{1}{a}\right) \div\left(1-\frac{1}{a…

05:08

In $15-26,$ find and graph the solution set of each inequality.$$2|x…

11:11

Amanda drove 40 miles. Then she increased her rate of speed by 10 miles per …

01:02

In $27-39,$ factor each polynomial completely.$$12 c^{2}-3$$

00:56

01:20

In $3-38$ , write each radical in simplest radical form. Variables in the ra…

00:45

In $3-12,$ write the sum or difference of the given polynomials in simplest …

02:24

In $9-26,$ write each expression as the product of two binomials.$$x…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.