Question

How do you solve rational equations? For example, (k+4)/4 + (k-1)/4=k+4/(4k). How do you check for extraneous solutions?

Answer 1

what is the LCM of k+4/4 and k-1/4 ???

Answer 2

Well, I was just wondering how to check for extraneous solutions. I've gimplified the equation to 8k^2+8k-16=0, but I'm not sure if that's right.

Answer 3

(k+4)/4 +(k-1)/4 =(k+4)/4k
(k+4+k-1)/4 = (k+4)/4k
(2k+3)/4 = (k+4)/4k
(2k+3)k = (k+4)
2k^2+3k=k+4
2k^2+2k-4=0
k^2+k-2=0

Answer 4

that looks correct

Answer 5

now try to factor k^2+k-2=0

Answer 6

OR u can use the direct formula

Answer 7

(k-1)(k+1)=0?

Answer 8

NO

Answer 9

k^2+k-2=0
k^2+2k-k-2=0
k(k+2)-1(k+2)=0
(k-1)(k+2)=0

Answer 10

does it help?

Answer 11

Yup, much thanks. However, what does it mean when it says "check for extraneous solutions"?

Answer 12

may be for imaginery solutions

Answer 13

How can you tell when you need to check?

Answer 14

if ax^2+bx+c=0 where b^2-4ac<0

Answer 15

but I am also not sure what extraneous solution means

Answer 16

Oh the discriminant

Answer 17

yes