options: Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
problem_activity: Problem 1
Below is the graph and equation of the function
$$f$$
.
$$f(x)=(x-2)(x-5)\over(x-2)(x+1)$$
[IMG]
And below is the graph and equation of the function
$$g$$
.
$$g(x)={(x-5)\over(x+1)}$$
[IMG]
How are the functions
$$f$$
and
$$g$$
similar Different?
Problem 2
How are the functions
$${g(x)}$$
and
$${h(x)}$$
different? Similar?
$${g(x)}={x^2\over{x-2}}$$
$${h(x)}={x^2-4\over{(x-2)(x+3)}}$$


correct_option_index: 0