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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.$$\frac{y+2}{2}+\frac{2 y-3}{3}$$

$\frac{7 y}{6}$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 4

Adding and Subtracting Rational Expressions

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

Oregon State University

McMaster University

University of Michigan - Ann Arbor

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In mathematics, the absolu…

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In $3-20$ , perform the in…

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we're being asked to add these two fractions, but we have a problem because in order to add or subtract fractions, we have to have a common denominator. And these do not is the first thing that we would need to do is try and find some number that both two and three can multiply up, too, so they're denominators would be in common. In this case, I would say the least common down to the lowest number of the two and three can both multiply up to would be six. So our goal right now is we want to rewrite both of these fractions so that they are over six. Then once we've done that, we can actually combine them together. All right, so let's start with why. Plus 2/2. If I want to get y plus 2/2 to be something over six, I would definitely need to take two times three. But if I'm going to take that denominator Times three, I would also need to multiply that numerator by the exact same thing, which means I'm going to take the quantity of Y plus two times three is well, that means we need to distribute that three, right? I know that's not written the way you're used to seeing it. Normally, you guys, we're used to seeing it written like this, but we would still want to. This is still a distributive problem, and so we still want to be using that property. So we'd be taking three times. Why gives us three why? And three times to gives us six. So we would have three y plus 6/6. So there's one fraction. Now I need to get the second fraction. That is to why minus 3/3. We also need to change that to something over six. Well, to get from 3 to 6, we would need to multiply by two. But if I'm gonna multiply the denominator by two that I would have to multiply the numerator by the exact same thing. This is a quantity of two y minus three. So that would mean we have a distributive property again. Two times two. Why would be four? Why, two times negative three would be negative. Six. Now that we have a common denominator, I can actually combine these. Remember, when we add or subtract fractions, we do not combine the denominators, we just rewrite it. Meaning it is still going to be over six for the numerator. We want to combine like terms. So I have a three y and a four y three y plus for why would be seven? Why? I have a six and I have a negative 66 plus negative six would be zero. Meaning we don't really need to write that. We just have seven. Why over six? There isn't anything that 76 have in common that I am aware of, which means we aren't able to reduce this fraction, so that would be an answer.

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