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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.$$a-\frac{3}{2 a}$$

$\frac{4 a^{2}-3}{2 a}$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 4

Adding and Subtracting Rational Expressions

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

Missouri State University

McMaster University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

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02:44

In $3-20$ , perform the in…

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06:54

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02:01

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03:39

first thing I noticed with this problem is that one term is written as a fraction and one term is not. I do not like trying to solve that math problems where I have different pieces being expressed in different forms. Just I think it just opens you up to accidentally making mistakes that you're better than so first thing I want to do is rewrite this and so that a can be represented as a fraction. I'm simply just going to put it over one. Right? A over one is certainly the same thing as a cause. Anything divided by one is itself. So that's that's fair. So I'm really doing a over one minus 3/2 A. All right now, I can see I do not have a common denominator here, so I'm gonna have to find one. Since one can be multiplied by anything, I'm not gonna need to multiply both fractions by something. I can already tell that I'm going to be able to just rewrite my second fraction because I should easily be able to get my fraction of a over one to change into a fraction that has to a for its denominator because I know that if I take one times to A, I will get to a now the catches just like with everything else we've been doing. If you want to change a rewrite a fraction and not change its value, whatever you multiply the denominator by you also have to multiply the numerator by meaning we have to take a times to a well a times to a would be to a squared right. Eight times a is a squared to is along for the ride Essentially. So my first fraction instead of a minus one could be expressed as to a squared over two A. I now have a common denominator, which means I am ready to combine these. Remember, when we combine fractions by adding or subtracting, we do not combine the denominators. We just rewrite it. That minus has nothing to do with the denominator, right. If you have a negative fraction, remember for a negative fraction, you can choose whether that negative is attributed to the numerator or the denominator. We don't want to put that negative to the denominator because then they wouldn't be in common, so instead just attributed to the numerator and will take to a squared minus three. Well, to a squared minus three would give me to a squared minus three right to a squared and three or not common terms. Not like terms. So I can't actually combine those. This just has to stay as a quantity. So this would be my answer. You can't reduce anything because everything in the numerator is together as a quantity. So unless you have exactly to a squared times three, then to a start here. So unless you have exactly to a squared minus three in the denominator, you would not be able to cancel it out. Okay, Now the last part of this, we do have to account for any undefined values for a So I looked back in my original problem. This a is a numerator, as we showed right here, so I don't need to worry about that. But I do have a denominator of to a So the question is, if I have to a what value of a would go would cause this equation to be zero, because that's what we don't want. Well, to time, zero would be zero. So the only problem for this equation would be if a happens to equal zero that would cause our answer to be undefined, which is basically just math word for an air. Right? So our answers to a squared minus three over to a as long as a does not equal zero.

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