How do you do this?

1/(1 - x) + 1/(1+√x) = 1/(1-√x)

2. Originally Posted by Trentt
How do you do this?

1/(1 - x) + 1/(1+√x) = 1/(1-√x)
1/(1-x)=1/(1-√x)-1/(1+√x)

1/(1-x)=(1+√x-1+√x)(1-x)=2√x/(1-x)

1=2√x

1/2=√x

x=1/4

3. Hello, Trentt!

Welcome aboard!

1/(1 - x) + 1/(1 + √x) .= .1/(1 - √x)

First, note that: .(1 - √x)(1 + √x) .= .1 - x

. . . . . . . . . .1 . . . . . 1 . . . . . . .1
We have: . ------ + --------- .= .--------
. . . . . . . . 1 - x . . 1 + √x . . . 1 - √x

Multiply through by (1 + √x)(1 - √x):

. . . . . 1 + 1 - √x . = . 1 + √x

And we have: . 2√x .= .1 . . √x .= .½ . . x .= .¼

4. Care to explain Perfect Hacker? I really have no clue what you're doing...

EDIT:Has been explained

5. Originally Posted by Soroban

Multiply through by (1 + √x)(1 - √x):

. . . . . 1 + 1 - √x . = . 1 + √x

Could you explain this step---this is the confusing part to me. And also can you explain why you chose (1 + √x)(1 - √x) to multiply the equation by?

6. Originally Posted by Trentt
Could you explain this step---this is the confusing part to me. And also can you explain why you chose (1 + √x)(1 - √x) to multiply the equation by?
Soroban multiplies through by (1+sqrt(x))(1-sqrt(x)) because:

1-x = (1+sqrt(x))(1-sqrt(x)),

so if you multiply both sides by this each of the terms leaves a simple
term in sqrt(x):

[1+sqrt(x))(1-sqrt(x)] [1/(1-x)]=(1-x)/(1-x) =1

[1+sqrt(x))(1-sqrt(x)] [1/(1+sqrt(x))]=(1-sqrt(x))

[1+sqrt(x))(1-sqrt(x)] [1/(1-sqrt(x))]=(1+sqrt(x))

so after multiplying through you are left with the equation:

1 + (1-sqrt(x)) = (1+sqrt(x)),

orL

2 sqrt(x) = 1

RonL