How to Teach Rational Expressions

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Teaching rational expressions will require you to pay close attention to the value of X. Teach rational expressions with help from an experienced math professional in this free video clip.

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Hi, I'm Drew Moyer. And this is how to teach rational expressions. Let's take a look at our problem. We have two over X minus X over eight equals three-fourths.The first thing I want to do, since I need to add and subtract these fractions. I need to make sure that they're all of the same denominator. So, I look at my denominators, I have X, eight and four. And I know that the common denominator must be eight-X. So, I want to multiply all the terms, top and bottom, until the denominator is equal to eight-X. So, I have two over X. And what do I need to multiply that by to make the denominator eight X? Well, it's missing an eight, but I need to multiply it by form of one. So, I don't change it. So, I multiply the whole thing by eight over eight. Next term is X over eight and if mu LCD is eight-X, I know that this is missing an X. So, I want to multiply this by X over X. And for the three quarters, I need to make it eight-X, so I know that it's missing two-X. So, I will multiply that by two-X over two-X. And then, I just want to carry out the multiplication. I have to times eight is 16 over eight-X minus X-squared over eight-X. And up top here, I have six-X over eight-X. And now, sine everything is over eight-X, I can then turn around and multiply everything by eight-X to get it to cancel out. So, I multiply this whole side by eight-X and this whole side by eight-X. And it will result in no fractions. So, I have 16 minus X-squared equals six-X. And now, from here, it's just solving a simple quadratic. So, I'm going to move everything over to the left side. Negative X-squared minus six-X plus 16 is equal to zero. I'm going to multiply everything by negative one, so that they don't leave with a negative. X squared plus six-X minus 16 is equal to zero. And then, factor this trinomial into two binomials. So, on this side, I would have X and X. And I need two factors of 16, looks like it's going to be eight and two. And the eight needs to be positive. So, it factors into X plus eight, X minus two. And that's because of zero product property, I know that either X plus eight must equal zero or X minus two is equal to zero. Solve this and I get X is equal to negative eight and I solve this and I get X is equal to two. So, I have two different answers for this quadratic. So, I'm Drew Moyer, and that is how to teach rational expressions.

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