One last Alg 2 Question...?

Question

Please write out all the steps so I know how you got to one step to the other...

How so I find all values of u satisfying the equation

- (12) / (u^2 - 8u + 16) =b (3u) / (u - 4)

(If there is more than one solution, separate them with commas.)

Thanks!

Correction on the equation...

- (12) / (u^2 - 8u + 16) = (3u) / (u - 4)

Answer 1

-12/(u-4)^2= 3bu/(u-4)
NB .. disallow u=4 as a solution

-4/b = u(u-4)
u^2 -4u = -4/b
(u-2)^2 = 4 -4/b = 4(b-1)/b
let c = 2sqrt( (b-1)/b)
(u-2)^2 = c^2
u = 2 + c, 2-c
Note : for real solutions b >=1 or b < 0

Answer 2

-12/ (u^2 - 8u + 16) = 3u / (u-4)

Factoring the perfect square trinomial u^2 - 8u + 16

-12/ (u-4)^2 = 3u / (u-4)

since 1/ (u-4) is common in both sides, we factor it out leaving us with:

-12/ (u-4) = 3u

cross multiply..

3u* (u-4) = -12

3u^2 - 12u = -12

3u^2 - 12u +12 = 0

u^2 - 4u +4 = 0

(u-2)^2 = 0

therefore, u = 2,2 OR u = 2 multiplicity 2

Answer 3

(12) / (u^2 - 8u + 16) =b (3u) / (u - 4)
-4(u-4)(u^2-8u+16)=bu
(u-4)^3=-bu/4

Answer 4

Alreday have answered several very similar to this. You just don't seem to be getting it. By the way, is the b following = sign supposed to be there?