Question

@mathmate

Answer 1

Yep.
Do you know direct and inverse variation?

Answer 2

no ._.

Answer 3

Direct variation is a function that varies directly with x.
For example
X Y
1 2
2 4
3 6
4 8
5 10

is a direct variation. Notice that Y/X is always the same ratio (of 2).
so far so good?

Answer 4

oh ok :)

Answer 5

On a graph, direct variation is a straight line passing through the origin.

Here f1(x), f2(x), f3(x) are all direct variations, but g(x) is not, because it does not pass through the origin.

Answer 6

ok with direct?

Answer 7

yes :)

Answer 8

For inverse variations, they work differently.
Y is the inverse (or reciprocal) of x. This way, X*Y is a constant (same number).
Example:
X Y
1 2
2 1
3 2/3
4 1/2
5 2/5
6 1/3
...
notice the product of X*Y is always 2.
the graph looks like this

Answer 9

ok for inverse variation?

Answer 10

Yes i get that :)

Answer 11

Can we move on the rational expressions?

Answer 12

* to

Answer 13

yes

Answer 14

A rational expression is a polynomial divided by another polynomial.

Answer 15

Example,
(5x+3)/(2x+1)
is a rational expression.

Answer 16

The sum of two rational expressions is also a rational expression, just like the sum of two fractions is still a fraction.

Answer 17

Even with one single rational expression, we can simplify , for example, what would be
\(\large \frac{(4x+3)(x-1)}{(x-1)}\) ?