Chapter 2, Section 2.5, Question 010 Suppose r(x) = (4x + 2)...

Chapter 2, Section 2.5, Question 010 Suppose r(x) = (4x + 2) / (x^2 + 1), s(x) = (x^2 + 6) / (6x - 1). Write the expression (r - s)(x) as a simplified ratio with the numerator and denominator each written as a fully simplified polynomial. Do not use parentheses and asterisks in your answer. (r - s)(x) =

Transcript

00:01 Okay, so for this problem, we want to find r minus s.

00:05 So we're going to take our r, and we're going to subtract r.

00:15 So we get something like this, and then we want to get them to have the same denominator, so we can squish these two fractions together.

00:29 So we're going to multiply this side by 6x minus 1, the top and the bottom, and this other side we're going to multiply by x squared plus 1, the top and the bottom.

00:43 This way they will have the same denominator.

00:49 I need to go to everything on the top and the bottom.

00:52 So i'll put parentheses there just to make it a little bit clearer.

00:56 So we need to foil all of these out.

01:01 So when we do that, over here we're going to have 24x x squared, sorry.

01:09 24x squared minus 4x plus 12x minus 2 and we're just going to leave these denominators factored.

01:20 We're not going to fill those ones out.

01:25 On this other side, we're going to have x to the 4th plus x squared plus 6 x squared plus 6x squared plus 6.

01:40 And again, we're just going to leave these denominators factored.

01:47 All right, so now they have the same denominator, we can squish these two fractions together.

01:54 Remember however though that this negative needs to go to all of these terms inside.

02:02 So we're writing this, we're going to have 24x squared, minus 4x plus 12x, minus 2, minus x to the 4th, minus x squared, minus x squared, and minus 6x squared, and minus 6.

02:19 And then we're going to have all of this divided by that denominator...

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