In Exercises 15–32, multiply or divide as indicated. (x^3−8)/(x^2...

Question

In Exercises 15–32, multiply or divide as indicated. (x^3−8)/(x^2−4) ⋅ (x+2)/3x

Accepted Answer

Welcome back. I'm so glad you're here. We've got this expression here, we've got two x minus three divided by X plus five times two X plus 10 divided by 14 X minus 21. And we are to do this operation the multiplication and then simplify. Alright, well we want to make sure everything is as factored as possible. We look at the 1st 12 x minus three over X plus five. That's as factored as it's going to get but this two X plus 10 that can be factored a bit. So let's copy down two x minus three over X plus five times and we can factor out a two. So two X now becomes X plus now becomes five. So we've got two times X plus five in the numerator. Now let's take a look at the denominator. Well we could factor out a seven. Both of those terms have a seven in them. So now instead of 14 X it's now seven times two X. And now instead of minus 21 it is now minus three and that is as factored as it's going to get. So now when it's factored, we want to look and see if we've got any factors in the numerator and the denominator that can cancel out. Well this is exciting because we've got a two x minus three in the numerator and a two x minus three in the denominator boom canceled those become ones. And look we've got an X plus five in the denominator here and an X plus five in the numerator here, boom canceled those are ones. So now, just multiplying straight across, we've got one times two times one. Well that's too and straight across the bottom. We've got one times seven times one. Well that is seven. That gives us an answer of 2/7 which matches our answer choice. A well done. We'll catch you on the next one.

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