1. ## (r-s)(x)

Suppose r(x) = 3+4/x^2+1, s(x)= x^+6/6x-1. Write the expression (r-s)(x) as a simplified ratio with the numerator and denominator each written as a sum of terms of the form cx^m and c>0 for the term with the highest power in the numerator. I ended up with (-x^4+11x^2+21x-10)/-6x^3+x^2-6x+1. Where did I go wrong here?

2. ## Re: (r-s)(x)

Without knowing the supposition, it is difficult to say where you went wrong.

3. ## Re: (r-s)(x)

This is the right answer but I don't know how to get it.

4. ## Re: (r-s)(x)

The links to images in your first post are broken for me.

Edited.

6. ## Re: (r-s)(x)

Originally Posted by Eraser147
Suppose r(x) = 3+4/x^2+1, s(x)= x^+6/6x-1.
Why not add 3 + 1 and simplify r(x) to 4 + (4/x^2)? And why do you write + in front of 6 in x^+6?

7. ## Re: (r-s)(x)

The only way I got the answer right was when I subtracted s with r instead of r - s. It looked like this with the polynomial subtraction (x^4 + 7x^2 + 6)-(18x^2+21x-4). And it gives me x^4-11x^2+21x+10 for the numerator.

8. ## Re: (r-s)(x)

Despite three request to write the question correctly, I am still doubting this has been done.

9. ## Re: (r-s)(x)

Here. it has to be correct. Just click on the image to enlarge.

10. ## Re: (r-s)(x)

\displaystyle \begin{align*}\frac{3x+4}{x^2+1}-\frac{x^2+6}{6x-1}&=\frac{(6x-1)(3x+4)-(x^2+1)(x^2+6)}{(x^2+1)(6x-1)}\\&=\frac{18x^2+21x-4-(x^4+7x^2+6)}{6x^3-x^2+6x-1}\\&=\frac{-x^4+11x^2+21x-10}{6x^3-x^2+6x-1}\\&=\frac{x^4-11x^2-21x+10}{-6x^3+x^2-6x+1}\end{align*}

11. ## Re: (r-s)(x)

Why are the signs flipped again at the end?

12. ## Re: (r-s)(x)

Changing the sign of both the numerator and the denominator (i.e., multiplying both by -1) does not change the fraction. The problem asks for a fraction with a positive leading coefficient in the numerator.

13. ## Re: (r-s)(x)

Originally Posted by Eraser147
Suppose r(x) = 3+4/x^2+1,

Do you mean 3+ 4/(x^2+ 1)?

s(x)= x^+6/6x-1.

What should be after the "^"? Do you mean x^?+ 6/(6x- )? Or (x^?+ 6)(6x- 1)?

Write the expression (r-s)(x) as a simplified ratio with the numerator and denominator each written as a sum of terms of the form cx^m and c>0 for the term with the highest power in the numerator. I ended up with (-x^4+11x^2+21x-10)/-6x^3+x^2-6x+1. Where did I go wrong here?

14. ## Re: (r-s)(x)

Oh, I already figured it out. Emakarov showed it. My mistake was not flipping the signs by multiplying -1 from numerator and denominator since the problem asked for the leading term to be a positive number and the constant to be more than zero. Read the post above to find the image of the actual equation if you are interested.