Question

Giving best answer, please help with this
Solve 4/(x^2-8x+12) = x/(x-2) + 1/(x-6)

Answer 1

@Noura11

Answer 2

4/((x-2)(x-6))=(x(x-6)+1(x-2))/(x-2)(x-6)
Denominators cancel out...
4=x(x-6)+1(x-2)
4=x^2-6x+x-2
4=x^2-5x-2
x^2-5x-6=0
hope u can do further.......

Answer 3

We have :
\[\frac4{x^2-8x+12}=\frac x{x-2}+\frac1{x-6}\]
So :
\[\frac{4}{x^2-8x+12}=\frac{x(x-6)+x-2}{(x-2)(x-6)}\]
So :
\[\frac{4}{x^2-8x+12}=\frac{x^2-6x+x-2}{x^2-6x-2x+12}\]
So :
\[\frac{4}{x^2-8x+12}=\frac{x^2-5x-2}{x^2-8x+12}\]
so we get simply :
\[x^2-5x-2=4\]
And this is simple equation, can you complete the solution from here ?

Answer 4

Could you tell me what you got just to be sure I got the sane answer? Not the best at this haha @Noura11

Answer 5

lol !
I think you should get
\[x=6\text{ or } x=1\]
So the solution is
\[S=\{6,1\}\]

Answer 6

That's incorrect. If you check it, you'll realize why

Answer 7

x=6 is undefined...

Answer 8

x^2-5x-6=0
x^2-6x+x-6=0
x(x-6)+1(x-6)=0
(x+1)(x-6)=0
x=-1,6

Answer 9

x=6 is undefined....

Answer 10

why?

Answer 11

1/(x-6)

Answer 12

ya....

Answer 13

when you cancel the denominators, you need to make note that x cant be 2 and x cant be 6

Answer 14

then,-1 is the answer

Answer 15

correct

Answer 16

as it satisfies the original equation.....

Answer 17

right

Answer 18

I was just explaining what @hero was referring to

Answer 19

okk....thanks @zzr0ck3r

Answer 20

@zzr0ck3r, you don't want to see my solution to this.

Answer 21

When I do it, I get exactly x = -1

Answer 22

Without having to deal with factoring a trinomial.

Answer 23

http://vyew.com/room#/418625/Math

Answer 24

would you have always solved it like that?

Answer 25

That's how I typically solve it, yes.

Answer 26

where are you from?

Answer 27

or where were you schooled rather?

Answer 28

I'm from the US. I don't know what you mean by school. But yeah, for the most part, I do develop my own methods. Some I steal from others.

Answer 29

im only asking because we all seem to go the exact same rout, and yours is so different.

Answer 30

this one I invented myself.

Answer 31

love it