Verified answer

(1+x) / (1-x) = (1+x)²

(1+x) = (1-x) (1+x)²

(1-x) (1+x)² - (1+x) = 0

(1+x) [ (1-x)(1+x) - 1] = 0

(1+x) [ 1 - x² - 1] = 0

(1+x) (-x²) = 0

-----------x value.

(1+x) = 0

x = -1

-x² = 0

x = 0

So, the answer for x (0, -1)

Regards,

1+x divided by 1-x

is equal to saying

1+x (times) 1 over 1-x

then you can can give them a common denominator. since 1+x is now over 1 (because it isn't a fraction like 1-x over 1 is) the common denominator is 1-x

now you have (1+x)(1-x) over (1-x) multiplied by (1) over (1-x)

If you do FOIL (multiplying first, outside, inside, last) with (1+x)(1-x) you will find you have 1 (- x + x) + x^2 or 1+x^2

now you have 1+x^2 over 1-x times 1 over 1-x. Since the denominators are the same, they cancel out. that is to say they don't even matter anymore. now you have (1+x)^2 times 1, which is just (1+x)^2

I'm sorry that I had to spell it out, because I don't know how to type all the small signs and things. If you are still confused, read each sentence outloud and write down what you hear in steps. Hopefully you will understand

Don,t divide by (1+x) It turns out (1+x)=0

(1+x)/(1-x)=(1+x)^2

(1+x) = (1-x)(1+2x+x^2)

1+x = 1+2x+x^2-x-2x^2-x^3

1+x = 1+x-x^2-x^3

0 = -x^2-x^3

x^2=-x^3

if x=0 then 0^2=0^3

if x is not = 0 we can divide by x^2

1=-x

so x=0 or x=-1

This was trickier than it first appeared

(1+x) = (1+x)^2 *(1-x)

(1+x) = (1+x) * (1+x) (1-x)

divide both sides with (1+x) ===>

1 = (1-x^2)

x^2 = 0

x = 0

only x = 0 can make the equation.

Agree with Turiski

It doesn't, except in the special case that x=0.