Simplifying Algebraic Fractions: Difference of Squares


Okay! So first of all, I took out the common factors for anything that I can. So here! See how x squared is common. So I took the x squared out and here, 16. We know that 16 is 4 squared. So this will be a difference of two squares.

So I’ve simplified it, like that. Now! Let’s use our cross method for the denominators, so you can see that one I’m going to use 4 which becomes 4x, and 5 which becomes 5x. Add them! We get 9x which is exactly what we want.

Now for this one, I’m going to use my x and x again. Now it’s negative, so I’m going to use positive and negative. So one’s going to be positive 3 and the other one will be negative 4, so negative 4x. And 3 minus 4x is negative x which is what we want. So now replace them all back into the denominators like that.

See how that one, I just left it as it is, and see how x squared minus 4 squared that’s x plus 4x minus 4, the difference of 2 squares and here, x plus 4, x plus 5 on the denominator and same for there, just replace them in. So now it’s my favorite part is to start canceling if anything that’s common. Now you can see that here, x minus 4 is common! Cancel! And you can see here, x plus 3, x plus 3 is common! Cancel! x plus 4, x plus 4, Common! Cancel them all out. So we just have x squared and x plus 5. That is the answer, okay?
So that’s just what’s left, so it’s nice and simple.


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