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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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.

Part of the Video Series: Math Skills

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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.