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all right what I like to do is a show

you how to find the thing made of a

problem like this no domain is very

tricky with us and one thing we're

finding domain couple things we need to

think about remember a function is when

you have an input value and you're able

to find an output that and that's what

we say is for it is defined for an

alphabet meaning if you put an input

value in you're going to get an output

value so there are a couple instances

though however when we plug in an input

value and there is no output value for

instance let's just set it f of X if I

did 3 over X well the only value that

this does not work for is when X is

equal to 0 because when x equals 0 I

have 3 divided by 0 and you cannot

divide 0 into a number so therefore we

write X cannot equal 0 so the domain for

this function I was gonna write the

domain it's gonna be all real numbers

all numbers negative 5 negative 13 107

all numbers work except for 0 so when

we're trying to find the domain of a

rational function what we want to do is

we want to find out what values making 0

on the bottom so here I have a quadratic

expression so I need to figure out x

squared plus 8x

plus 15 equals zero I want to figure out

what values can I find for X that are

going to make this function zero so when

we have a quadratic it's a little bit

difficult it's not like a regular linear

equation where you can just solve for x

we're gonna have to do some type of

either squaring or factoring since I

have two x's I know that I'm going to

want to do factor so what type of

factoring I want to do well here my a is

equal to 1 B is equal to 8 and C is

equal to 15 so a lot of times what I'll

do is always take my 8 times C which is

1 times 15 and I'll take my B which is 8

and I'm just gonna systematically think

of what two numbers multiply to give me

15 but add to give me 8 and those

answers are gonna be 3 and 5 so

therefore I can factor this to be X plus

3 times X plus 5 equals 0 and if I was

to foil this back out I would get this

expression now either one of these

multiply to give me 0 so therefore one

of these has to be 0

so you can say X plus 3 equals 0 or X

plus 5 equals 0 therefore if subtract 3

if X is equal to negative 3 this problem

equals 0 or if X is equal to a negative

by this problem sequels here so if you

were to plug in negative 3 into there

you would get 0 if you're plugging in

negative 5 into this equation you would

get 0 so therefore my domain for this

problem

is going to be all real numbers except X

cannot equal a negative three and a five

so when you're defining the domain

especially the rational expression you

want to see what numbers can't we use

and the numbers you can't use are the

numbers that are going to make our

denominator zero