Question

Algebra II: Solving rational equations help, will medal (equation attached)

Answer 1

\[\frac{ k+1 }{ k }=1-\frac{ k^2-3k-4 }{ 4k }\]

Answer 2

get rid of those fractions by multiplying everything by a common denominator, 4k is easiest, what does that get

Answer 3

the goal is to isolate k, k = ...

Answer 4

4k+4=4k-k^2+3k+4

Answer 5

so...

Answer 6

yes , looks good

Answer 7

and now I do what with this newfound info?

Answer 8

subtraction and addition , take 4k off both sides....

Answer 9

I've gotten to:

Answer 10

\[k^2+4k+4=7k+4\]

Answer 11

yes that all looks fine...
notice both sides have +4, that cancels, ( -4 both sides)

Answer 12

\[k^2=3k\]

Answer 13

good, now what

Answer 14

that's where I have not a clue

Answer 15

you can do anything you want to the equation, as long as you do it to everything both sides,
try multiplying by 1/k, same as dividing by k

Answer 16

k=3?

Answer 17

right!
you could also argue k=0 from

k^2=3k
k^2-3k=0
k*(k-3)=0

k=0
or
k-3=0

if you don those, but testing k=0 in the original problem will give you a 0 denominator, which is not defined, and not a solution

Answer 18

extraneous

Answer 19

I see, thank you!

Answer 20

welcome