Question

Please help will medal!
Simplify the rational expressions. state and excluded values

Answer 1

\[\frac{ x+7 }{ x^2+4x-21 }\]

Answer 2

@cwrw238

Answer 3

Hello alice, have you figured it out already?

Answer 4

Hello N00bstyle no i havent

Answer 5

Are you familiar with the 'sum-product-rule'?

Answer 6

no...

Answer 7

If you look at the denominator, you can write that expression differently

Answer 8

Ask yourself the question: what two numbers do I need to add to get '+4', while when I multiply those two numbers I get '-21'

Answer 9

It's like a little puzzle, which you have to solve many times more ;)

Answer 10

lol thats a nice way to think about it

Answer 11

Let me help you out, try the numbers '-3' and '+7'

Answer 12

When you add those numbers you get +4, and when you multiply them you get -21

Answer 13

ohhhh i see now

Answer 14

The point is to reformulate the expression in the denominator.
So x^2 + 4x - 21 can then be written as:
(x - 3) * (x + 7)

Answer 15

Now the formulate can be written as:
(x+7)/((x-3)(x+7))

Answer 16

\[\frac{ x+7 }{ (x-3)(x+7) }\]

Answer 17

Now since both the numerator and the denomiator have 'x+7' in it, you can divide that part

Answer 18

okay do the x+7 cancel out?

Answer 19

this leaves you
\[\frac{ 1 }{ x-3 }\]

Answer 20

idd, very good

Answer 21

c: okay

Answer 22

thank you

Answer 23

as you probably already know, it is not allowed to divide by zero, so which number will give you an asymptote?

Answer 24

I mean: there is an x in the denominator of the formula we derived

Answer 25

And when that x becomes a value which is equal to a number so the denominator results in being zero, then that value of x will be an asymptote

Answer 26

so in this case the asymptote will be at x = 3

Answer 27

that makes sence

Answer 28

In the future, see these quadratic functions (x^2 + ... - ...) as little puzzles, and apply the sum-product-rule

Answer 29

I will

Answer 30

then you have a function written between brackets, and then a lot of times parts will cancel out

Answer 31

good luck

Answer 32

this was very helpful thank you