I dont understand shi--

[rough fox]

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[dry mauve]

Firstly we want to factor it

Do you know how to do that

[alpine matrix]

No I dont know how to do that

😦

[unreal flower]

😭

[dry mauve]

Do you know what difference of squares is

Basically

[alpine matrix]

now how did this happen

[unreal flower]

Put $ at the front too

[alpine matrix]

oh my god what was i doing

my entire life

can you please elaborate

[dry mauve]

$x^2 - 1$ can be factored as $(x-1)$$(x+1)$

[thorn berry]

CaliforniaJumpingBean

[dry mauve]

Do you see that

[alpine matrix]

yeah

but how did this happen

[dry mauve]

Wdym how

[alpine matrix]

where did the x-1 and x+1 came from

i dont know how to factor

[dry mauve]

So the first term is x^2, the middle term is 0x, and the last term is -1

So the middle is canceled

Therefore we have factors that are the same, except for the opposite sign

And since the last term is -1

We know the factors are -1 and 1

Idk

Do you get that?

We can also factor the bottom similarly

[alpine matrix]

wait

let me process this

[alpine matrix]

how

[dry mauve]

Since the last term is -1 right

So in this method

[alpine matrix]

how is x^2 and -1 same

[dry mauve]

No

[alpine matrix]

sorry for my low iq actually i am not a math student

[dry mauve]

-1 and 1

[dry mauve]

That makes the (x-1) and the (x+1)

So

Basically

We look at the first term for x

It is a singular x

[alpine matrix]

yeah

[dry mauve]

So the only choices for the coefficients are 1 and 1 right

[alpine matrix]

yeah

[dry mauve]

(x+a)(x+b) where a and b are unknown as of this step

Ok

[alpine matrix]

aight

[dry mauve]

So we have no middle term right

[alpine matrix]

yeah

[dry mauve]

And the last term is -1

So there is only 1 combination of a and b that works

-1 and 1

[alpine matrix]

ohh

another question

[unreal flower]

honestly factoring the top part doesn't really matter

[alpine matrix]

why we use two signs - and + why not negative or positive both sides

[unreal flower]

it's the bottom part that you should factor

[unreal flower]

difference of squares in general, $x^2-a^2=(x-a)(x+a)$

[thorn berry]

Anonymous

[alpine matrix]

i cant even do the basic how will i factor that denominator T_T

[unreal flower]

just try and distribute and you can convince yourself this always holds true

[dry mauve]

So

[dry mauve]

Do you know the quadratic formula

Or grouping

[unreal flower]

I suggest you watch some sort of video and learn that first. It's hard to do these problems with that skill.

[alpine matrix]

yeah

ik that

[unreal flower]

but the idea for factor $x^2-7x+12$ is you find two numbers whose product is 12 and sum is -7

[thorn berry]

Anonymous

[alpine matrix]

x = -b+- root b^2*4ac/2a

[dry mauve]

Can you try this

[alpine matrix]

wait wait this is way too hard for me

let me do it

[alpine matrix]

should i use quadratic formula to solve this

[unreal flower]

try and think about it first

[unreal flower]

no

i mean you can but this is much faster

[alpine matrix]

okay

wait

let me factor it myself

tell me if i am wrong

[dry mauve]

Good luck with this problem

[dry mauve]

I'll leave it up to you to help

[alpine matrix]

understood

[dry mauve]

I think 2 of us isn't helpful

[alpine matrix]

(x-3)(x+4)

[unreal flower]

ya sorry i kinda just interrupted from nowhere though 😭

[unreal flower]

whats -3+4

[alpine matrix]

1

[unreal flower]

well that's not -7

[alpine matrix]

oh

wait

(x-3)(x-4)

[unreal flower]

perfect

[alpine matrix]

less go

[unreal flower]

here's how I'd approach this problem:

$\frac{x^2-1}{x^2-7x+12} \ge 1$ \
$\frac{x^2-1}{x^2-7x+12}-\frac{x^2-7x+12}{x^2-7x+12}\ge 0$ \
$\frac{7x-13}{(x-4)(x-3)}\ge 0$

[alpine matrix]

huh

[thorn berry]

Anonymous

[unreal flower]

I subtracted 1 from both sides and got a common denominator so that i can add the fractions

[alpine matrix]

so did you cross multiply denominator with 1 to get it common

[unreal flower]

it's not really cross multiplying

you just want the bottom part to be the same

[alpine matrix]

i didnt understood after subtracting 1 from both sides , how did you got same denominator

[unreal flower]

i multiplied the top and bottom by x^2-7x+12

[alpine matrix]

wow

are we allowed to do that

[unreal flower]

well notice, what is $\frac{x^2-7x+12}{x^2-7x+12}$ equal to? the same number divided by itself

[thorn berry]

Anonymous

[alpine matrix]

yeah

[unreal flower]

well, what is it?

[alpine matrix]

1 ?

[unreal flower]

yes, so it's the exact same as before

just a different way of writing it

[alpine matrix]

which way do you prefer

i think that one was easier

for me

[unreal flower]

yes but you can't add the fractions if the bottom term isn't the same

[unreal flower]

if you just had 1 you can't add that

[alpine matrix]

should i use the wavy curve method to further solve this ?

[unreal flower]

i do not know what that is

[alpine matrix]

waa--

aight

ty for ur time sir

[alpine matrix]

its like a signchart to find out the intervals

[unreal flower]

i have my own way of doing it which is pretty fast but i'm not sure if it'll help you or confuse you more

[alpine matrix]

oh cmon

make me understand

[unreal flower]

if you want to, sure

[alpine matrix]

i dont want to waste time on long methods

but please elaborate while explaing cuz i am just dumb

[unreal flower]

dash lines means negative, bold lines means positive

if you are familiar with the quadratic and linear functions,
(x-4)(x-3): you know that it's negative in between the roots and positive everywhere else
(7x-13): the line is positive for anything above its root (13/7) and negative everywhere below it
multiply the signs of both regions, and you get your desired result

it's like the same process of how people normally do it, except if you understand the functions well enough you don't need to plug anything into your calculator

[tiny coral]

bring one to this side, make it into a single fraction, create factors, check od powered factors for their zeroes and plot it on number line using wavy curve

[unreal flower]

never understood why people just restate the already answered

[alpine matrix]

well i didnt knew that one

thanks for explaining it was really helpfull ^^

[alpine matrix]

i solved it ty