Answer:
[tex](u/v)(x)=-x^{3}+x^{2}-1[/tex]
Step-by-step explanation:
The arithmetic operation of the two equations presented in this case can be solved as a division of polynomials.
We can write the problem as:
[tex](u/v)(x)=\frac{u(x)}{v(x)} \\\\(u/v)(x)=\frac{x^5-x^4+x^2}{-x^2}[/tex]
We need not to forget the negative in the denominator. Then we can factor the numerator as follows:
[tex](u/v)(x)=\frac{(-x^2)(-x^3+x^2-1)}{(-x^2)}[/tex]
Now we can easily spot the solution, and get there with the following steps:
[tex](u/v)(x)=(\frac{-x^2}{-x^2}) (-x^3+x^2-1)\\\\(u/v)(x)=(1)(-x^3+x^2-1)[/tex]
As I said earlier we need to remember that the negative will change the symbols in the equation once we factor the polynomial.
And like that we get to the answer:
[tex](u/v)(x)=-x^{3}+x^{2}-1[/tex]
