Question

can you check me? (Alg II rational equations) I medal!

Answer 1

\[\frac{ 21 \pm \sqrt{-1,169} }{ 2*7 }\]

Answer 2

original equation:\[\frac{ 6 }{ x-1 }=\frac{ 4 }{ x-2 }+\frac{ 2 }{ x+1 }\]

Answer 3

Multiply both sides by x-1
\[\frac{(x-1)*6}{x-1} = \frac{(x-1)*4}{x-2} + \frac{2*(x-1)}{x+1}\]

Answer 4

(x-1) gets cancelled in the left side of the equation
Multiply both sides by x-2 and x+1
\[6(x+2)(x+1) = \frac{4(x-1)(x-2)(x+1)}{(x-2)} + \frac{2(x-1)(x-2)(x+1)}{(x+1)}\]

Answer 5

Did you do the following?

Answer 6

yes

Answer 7

It looks like all the x's get cancelled

Answer 8

How did you get an irrational number for your x

Answer 9

because after you finish cancelling then you have to foil the rest of the parenthesis to get 7x^2-21x+26, and since that doesn't factor I need to use quadratic formula

Answer 10

\[6(x-2)(x+1) = 4(x-1)(x+1) + 2 (x-1)(x-2)\]

Answer 11

\[6x^2-6x+12 = 4x^2 -4 +2x^2 -6x + 4\]

Answer 12

Do you see what I mean

Answer 13

okay yes, I do

Answer 14

A solution doesn't exist for this problem

Answer 15

that makes perfect sense! thank you!

Answer 16

I messed up one number and then I sent myself down quadratic formula road :/

Answer 17

That happens! Glad you've finally understood :)

Answer 18

let me know if you need any help!

Answer 19

To be honest I hope I don't. But if I do I know who to reach :)

Answer 20

Goodluck!

Answer 21

... and I'm back @thushananth01 :/ soo how did you get 12? I got -12

Answer 22

Shoot! That's a -12, you are right, but that does not change the coefficient of x or x squared

Answer 23

so it will still cancel all?

Answer 24

It will cancel all the x's and x squared
\[6x^2-6x-12 = 4x^2-4+2x^2-6x+4\]
\[(-4x^2 - 2x^2) +6x^2- 6x -12 = 4x^2-4+2x^2-6x+4 +(-4x^2-2x^2)\]

Answer 25

\[-6x - 12 = -4 -6x +4\]
Now 6x will get cancelled
you will end up with
\[-12 = 0\]
which is absolutely not a solution

Answer 26

I don't follow... what are those parenthesis?

Answer 27

@thushananth01

Answer 28

The paranthesis shows that I am subtracting -4x^2 -2x^2 in both sides

Answer 29

ooh I see I thought it was multiplication

Answer 30

No, did you understand ?

Answer 31

I do now :D