WEBVTT
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did a lot this semester.
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Okay, now you need probably scratch paper to figure out how to factor each of these
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and again any method you want to use will be fine as long as you're sure you factor correctly
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which you know whether you factor it correctly by multiplying it back out.
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All right, so that's the first thing we need to do for both of these.
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You cannot cancel until it's each both the numerator and denominator are factored.
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So this is 3x and that's x.
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And you know this is going to be a 2x and an x.
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All right, with multiplication and division you still need to have everything factor before you can cancel.
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With division you're going to have to multiply by the reciprocal first.
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So on this first problem remember all of these things need to be factored if possible.
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So x minus 3 can't do anything more without.
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But out of 8x plus 2 you could take a 2 out so that's a factor and 4x plus 1.
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And let's see out of the denominator you can factor out an x and that gives you 4x plus 1.
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And x squared minus 9 is a difference of 2 squared is x plus 3 and x minus 3.
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So you have to go through all that and I'll see if there's some common factors.
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So the x minus 3 cancels with that x minus 3, the 4x plus 1 cancels without 4x plus 1.
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So I'm left with the 2 at the top.
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There we go.
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Should be an x and there we go.
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Okay now the first thing you do over on this left side is multiplied by the reciprocal.
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So I have x squared minus 2x over 15 times the 5x over x minus 2.
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And now we proceed by factoring just like we did on the left side.
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So these are factors.
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Now if you want you can cancel that 5 and 15 right now or we could do it later.
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So I'm going to factor the x out of the x squared minus 2x.
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And I'm going to write this as times 5 times x.
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So it's easy to see all the separate factors.
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And I'm going to write the 15 as 3 times 5.
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You can leave it as 15 and cancel.
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It gets the same thing.
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And now I see what I can cancel x minus 2s go.
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And the 5s go.
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And so what I have left on the top is the next times the next x squared.
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And the denominator all I have is a 3.
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So I have x squared over 3.
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By the way, part A if you want you could multiply the denominator out and leave it as x squared plus 3x.
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That's also fine.
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Either way, it's correct.
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Okay, we're adding.
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Now we don't really add if we have a common denominator.
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And luckily in A and B we've got common denominators.
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We need to add the numerators.
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So we have 4x plus 5 added to 8x plus 5.
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And the denominator is just stays the same.
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You do not add the denominators.
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So that gives me 12x plus 10 over 6x plus 5.
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And no, you cannot cancel the 10 and the 5 or the 6x and the 12x.
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You have to factor.
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All right, so I could factor 2 out of the top.
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And that's a 6x plus 5.
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And I can't factor out of the bottom.
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But how convenient.
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6x plus 5s cancel.
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And so my answer is just the number 2.
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All right, let's go to the second one.
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This is a little bit trickier because of the minus sign here.
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You're going to have to subtract the whole numerator here.
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So be careful.
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You've got x squared plus 3x minus an x squared minus 12.
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All over, you just write the denominator down.
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Do you know what?
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Add the denominators.
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So have x squared plus 3x minus x squared.
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Plus, last 12 because you have to distribute that minus sign.
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All right, well, now in the numerator, the x squared minus x squared.
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That's gone.
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So I have 3x plus 12 over x squared plus x minus 12.
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Now we need to factor.
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So out of the top, you can factor out at 3 and at the bottom.
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You're going to have an x plus 4 times the next minus 3.
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And the x plus 4s are going to cancel.
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So when all is said and done, you're going to get 3 over x minus 3.
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So I'm going to write 3 over x minus 3.
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And you cannot cancel those 3s.
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Leave it be.
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OK.
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Almost done.