In Exercises 33–68, add or subtract as indicated. x/(x^2−2x−24) −...

Question

In Exercises 33–68, add or subtract as indicated. x/(x^2−2x−24) − x/(x^2−7x+6)

Accepted Answer

Welcome back. I'm so glad you're here. We are given this expression it's two X divided by 30 X plus plus five divided by 10 x plus 34. Alright well we want to add these they need a common denominator and these look kind of similar. Let's see if we can factor these denominators to see if they have anything in common. Looking at the one on the right hand side, 10 X plus 34. All we're going to be able to bring out of that is a two which will leave us with a five X plus 17. So there's a lot we could factor out of 30 but let's get that 30 X to look like a five X. So let's factor out of six. So that'll leave us with five X. And 102 divided by six is 17. Ding Ding ding. They both have a factor of five X plus 17 in common. And now we've just got them to have that six in common. So we can look at the right hand fraction and we can multiply that by 3/3 because that's just one. We're not changing it. So let me rewrite that down here so you can see what we're doing. So we have two X over six times five X plus 17. The factored version plus a five times three divided by two times three Times five x plus 17. Because when we do that multiplication, bringing over the left hand fraction. Keeping it factored in the denominator plus. Now let's do the multiplication five times three is 15, divided by two times three is six times five X plus 17. C. There Now we've got a common denominator and we can go ahead and add straight across the top two X plus 15 is two X plus 15. They are not like terms they can't combine and our common denominator denominator is six times five. X plus 17. We can't factor anything out in the numerator to see if anything cancels out one of the factors in the denominator that's as simplified as this one is going to get we look at our answer choices and this matches with answer choice C. Well done. We'll catch you in the next one.

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