homework help - PLEASE - how do i get to that step??

Question

i'm taking a linear algebra class and i have the concepts down but the algebra is killing me!! how do i get from:

V = (2V) / (1-V^2)

to

(V+V^3) / (1-V^2) ???


Can anyone explain what in the world happened???

THANKS!!!!

math links welcome

any help is desired

thanks!

Answer 1

0=(2v)/(1-V^2)-v
=(2v)/(1-V^2)-v(1-V^2)/(1-V^2)
=(2v-v+V^3)/(1-V^2)
=(v+V^3)/(1-V^2)

Answer 2

You can't. Your first expression is an equation (it has an equals sign in it). Your second expression is just that, an expression. There's no equals sign.

The solutions to the original equation can be found as follows:

V = (2V)/(1-v^2)

Multiply both sides by (1-V^2):

V - V^3 = 2V

Bring all the terms to one side of the equals sign:

V+V^3 = 0

Factor this:

V*(1+v^2) = 0

V = 0 is the only real-valued solution to this equation. If you admit imaginary solutions, then V = +i and V = -i are also solutions.

Answer 3

V = (2V) / (1-V^2)
By cross mutilication
V -V^3 = 2V
0 = V^3 + V
Therfore
(V+V^3) / (1-V^2)=0

Answer 4

I'm assuming you want the second expression to equal 0, since it works out that way...

V = 2V/(1-V^2)
0 = 2V/(1-V^2) - V
0 = 2V/(1-V^2) - [V*(1-V^2)]/(1-V^2)
0 = 2V/(1-V^2) - (V-V^3)/(1-V^2)
0 = (2V-V+V^3)/(1-V^2)
0 = (V+V^3)/(1-V^2)

Answer 5

Looks more like Algebra I than Linear Algebra.

Linear Algebra involves systems of linear equations, matrix algebra, etc.

Answer 6

i have to go to groceries
but under stand that there is a 1 = (v+V a3)/(1-va2)
i cant write exponetials

Answer 7

first one is an equation, second one is just an expression. you can't get from one to the other.

Answer 8

sorrrrrrrrrrrrrrrrrrrrrrrry