Fractions involving Quadratic and Linear Terms: Difference of Squares

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It’s a square number minus the square number because you know that 16 is 4 squared, so it’s going to be, let’s get, as I said, 4 squared. So square minus square, how do we factorize that? Everyone should know it will be x plus 4, x minus 4, okay? Or the other way around, it doesn’t matter, okay? So you can see that x minus 4 is common, cross them out. So we have x plus 4 left, okay? So here, we don’t need to use the cross method because you should all remember how to factorise the difference between two squares. Okay?

Question 9. Okay! Let’s go ahead and do this. First of all, numerator, I can’t do much, but denominator, you can see that 27 and 3. 3 is a common factor but what I’m going to do is swap these around because I want my x square to come first because I always don’t know that’s the way I like to put it. I always want the x squared to come first. I always want it in order x squared x and then the constant. So that’s why I switch things around, and as I said, guys, 3 is a common factor but remember, I don’t want to have a negative in front of my x squared.

So I’m going to factorize by negative 3. So that becomes a positive x squared, which switches to a negative, so negative 9, okay? And now, guys, look at the brackets; look inside the brackets. We’ve got x squared minus 9, a difference of two squares, so 9 is 3 squared. So the difference of two squared squares minus squares. So how do we factorize that? All of you should tell me, x plus 3, x minus 3, okay? So I can cross these out, yeah? So we have that left; 1 make sure you put 1 on the numerator, 1 over negative 3x plus 3. Okay?

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