Question

Can someone explain these two?

Answer 1

I believe you cancel out values if there are the same ones for the numerator and dominator.

For example:

`(x^4+x^2+x-3)/(x^4+x^3-3)`

Since both the numerator and dominator have
`x^4` and -3, you are able to cancel them out.

This would leave you with
`(x^2+x)/(x^3)`

Notes: the exponents have to be the same number in order to cancel out the values.

Answer 2

11. C) x +1

12. B) x -1

Explanation:

You want the simplified form of a couple given rational expressions.

Each of the polynomials can be factored by pairs. Common factors can be cancelled.

11.

Factoring numerator and denominator pairwise, we have ...

`(x^3+2x^2-x-2)/(x^2+2x-x-2)=(x^2(x+2)-1(x+2))/(x(x+2)-1(x+2))=((x^2-1)(x+2))/((x-1)(x+2))\\\\=(x^2-1)/(x-1)=((x+1)(x-1))/((x-1))=\boxed{x+1}`

12.

Factoring the numerator pairwise,, we have ...

`(x^5-x^4+x^3-x^2+x-1)/(x^4+x^2+1)=(x^4(x-1)+x^2(x-1)+1(x-1))/(x^4+x^2+1)\\\\=((x^4+x^2+1)(x-1))/((x^4+x^2+1))=\boxed{x-1}`