Question

Simplify completely quantity 12 x plus 36 over quantity x squared minus 4 x minus 21 and find the restrictions on the variable.

Answer 1

@amistre64 @Hero @Mandre

Answer 2

can you factor the top and bottom ?

Answer 3

I tried... I think it's wrong

Answer 4

can you factor (12x+36) ?

Answer 5

6(2x+6)

Answer 6

yes, but notice you can go even further

Answer 7

or 12 maybe

Answer 8

12(x+3)

Answer 9

yes, now the bottom
x^2 -4x -21

first list all pairs of number that multiply to give you 21
1,21
3,7

are all of them
the - on the -21 means they will have opposite signs
the -4x means they add up to -4
which pair should you use ?

Answer 10

3 and -7?

Answer 11

so the factors are (x+3)(x-7)

you have
\[ \frac{12(x+3)}{(x-7)(x+3)}
\]
do you see what you can "cancel"?

Answer 12

x+3

Answer 13

so we get 12/x-7?

Answer 14

how do we find the restrictions?

Answer 15

yes , but use parens: 12/(x-7)

now
find the restrictions on the variable.

you do not want to divide by zero. in the original you were dividing by
(x+3)(x-7)
so you should not let x be certain values or you will get a zero
what should x NOT be ?

Answer 16

7

Answer 17

yes. because (x-7) with x= 7 gives (7-7) = zero
and (x+3)(x-7) becomes (7+3)*0 = 0 and we do not want to divide by 0

but there is another x that makes the bottom zero.

Answer 18

I don't know

Answer 19

if x+3 is 0, the bottom becomes zero

Answer 20

-3?

Answer 21

yes. you could "solve" this by saying
either
x-7= 0
add 7 to both sides
x-7 +7 = 0 +7
x +0 = 7
x=7

or

x+3= 0
add -3 to both sides
x+3-3= 0-3
x= -3

so exclude x=-3 and x=7, because they would cause divide by 0

Answer 22

Okay, I think I get it now :D do you think you think you could help me with the trinomial factoring again, though? I'm still a little sketchy on that. Let's say I have x^2-15x+36, how would I factor that? I can't think of any numbers that multiply to 36 and add to -15...

Answer 23

look at the +36
list all the pairs that multiply to give 36
it helps if you (1) know the multiplication table (2) know some "divisibility rules"
see https://en.wikipedia.org/wiki/Divisibility_rule#Divisibility_rules_for_numbers_1.E2.80.9320
I learned the rules for 2,3,4,5,6

can you list all pairs for 36 ?

Answer 24

1 36, 2 18, 3 12, 4 9, 6 6

Answer 25

yes, now the + sign on the 36 means the factors have the same sign
(- means the factors would have different signs)

the -15x means the larger factor is minus (so that means both factors are minus)

they add to -15
which pair, when both numbers are minus, add to -15 ?

Answer 26

ohhhh okay, so it would be -12 and -3?

Answer 27

so you have (x-12)(x-3) as the factors

multiply out to check: x^2 -12x -3x +36 = x^2 -15x +36

Answer 28

if you make notes on how to do it, do a bunch of examples, you will learn how to do it.

Answer 29

okay, thanks!