Simplifying Rational Expressions

Video Transcript

"Lets take a look at simplifying a rational expression. So rational expression just means that we have variables on the bottom of a fraction. Rational expression is a technical math term for variables on the bottom of a fraction, as well as on the top or not it doesn't matter. But being on the bottom makes it a rational expression. So if we want to simplify this expression, the key is we are going to factor this top part and see if we can cross cancel something, if we can simplify it. Just like simplifying a fraction. You know if we had like two x over x, you cancel out the x's that's simplifying that fraction, it would become two, same thing here. So the top part can factor, the top part is going to become, so this guy here we are going to factor it, so x squared minus three x plus two, we are going to put an x here, and and x here. We need two numbers that multiply to be two but add to be three. The only options are two and one. Two times one is two. And sure enough, two and one can combine to make three. So we are going to have minus two minus one. X minus two minus x minus one foils out to be this. And then on the bottom we have x minus two, now just like in this example here, we have something on the top and bottom that simplify out. X minus two and x minus two cancel out. Leaving me x minus one, so this rational expression simplified is simply x minus one."