Exercises 57–59 will help you prepare for the material covered in...

Question

Exercises 57–59 will help you prepare for the material covered in the next section. Add: (5x−3)/(x^2+1) + 2x/(x^2+1)^2.

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression two x minus one over X squared plus nine plus five X over X squared plus nine squared. We're asked to find the sum or to add these two fractions together. Well, in order to add two fractions, we need to have a common denominator and these are very close. They're already factored and both of them have this factor of X squared plus nine. It's just that the second one has two X squared plus nines. As we see by the fact that X squared plus nine is squared. So in order to have a common denominator, we just need to multiply this first one by X squared plus nine. So we'll now have two of them in the denominator. And what we do for the denominator we also need to do for the numerator because X squared plus nine over X squared plus nine. That's essentially one. So we're just multiplying that first fraction by one. So I'll rewrite that X squared plus nine times two X minus one in the numerator. And then we have X squared plus nine squared in the denominator plus our five X over X squared plus nine squared. Now they do have a common denominator and we could combine them but at this point I want to foil out this numerator for the left hand fraction. So X squared plus or times two X is going to be a two X cubed and our outsides X squared times negative one will be a minus X squared and our insides nine times to X will give us a plus 18 X. And for our last nine times negative one will be minus nine. Still over X squared plus nine squared plus five X over that same denominator, X squared plus nine squared. All right now we can combine our numerator and combine our denominators because they're the same. So the denominator is X squared plus nine squared. The numerator will just start copying down the left hand side two X cubed minus X squared plus 18 X minus nine. And then plus five X. Now to combine like terms and the only two like terms in the numerator are this plus 18 X in the plus five X. So when we combine this we'll have two x cubed minus X squared plus 18 X plus five X 23 X minus nine over R x squared plus nine squared. That's as simplified as it's going to get. We look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one

Exercises 57–59 will help you prepare for the material covered in the next section. Add: (5x−3)/(x^2+1) + 2x/(x^2+1)^2.

Key Concepts

Rational Functions

Common Denominator

Polynomial Addition

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