Question

Can someone explain these two?

Answer 1

Answer:

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

For example:

$\frac{x^4+x^2+x-3}{x^4+x^3-3}$

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

This would leave you with $\frac{x^2+x}{x^3}$

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

Answer 2

Answer:

  11.  C) x +1

  12.  B) x -1

Step-by-step 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 ...

  $\dfrac{x^3+2x^2-x-2}{x^2+2x-x-2}=\dfrac{x^2(x+2)-1(x+2)}{x(x+2)-1(x+2)}=\dfrac{(x^2-1)(x+2)}{(x-1)(x+2)}\\\\=\dfrac{x^2-1}{x-1}=\dfrac{(x+1)(x-1)}{(x-1)}=\boxed{x+1}$

12.

Factoring the numerator pairwise,, we have ...

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