r(x)=3x+5/x^1+1, s(x)=x^2+3/3x-1
write the expression (2r-3x)(x) as a simplified ratio with the numerator and denominator each written as a sum of terms of the form cx^m and c0, for the term in the highest power in the numerator
(2r-3s)(x)=f(x)/g(x) where f(x)=? and g(x)=?

Question

r(x)=3x+5/x^1+1, s(x)=x^2+3/3x-1
write the expression (2r-3x)(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 in the highest power in the numerator
(2r-3s)(x)=f(x)/g(x) where f(x)=?  and g(x)=?

anonymous · Answer

is that really 
$$x^1+1$$ in the denominator of the first one?

anonymous · Answer

let me doucle check

anonymous · Answer

x^2+1

anonymous · Answer

$$2\frac{3x+5}{x^2+1}=\frac{6x+10}{x^2+1}$$

anonymous · Answer

$$3s(x)=3\frac{x^2+3}{3x-1}=\frac{3x^2+9}{3x-1}$$

anonymous · Answer

my bad

anonymous · Answer

subtract and get 
$$\frac{-3 x^4+6 x^2+24 x-19}{(3 x-1) (x^2+1)}$$

anonymous · Answer

the way you answered, I'm slightly confused.  could you put the answer in f(x) and g(x) form?

anonymous · Answer

assuming my algebra is correct, 
$$f(x)=\text{numerator}$$ 
$$g(x)=\text{denominator}$$

anonymous · Answer

$$f(x)=-3 x^4+6 x^2+24 x-19$$ in other words