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Anonymous Sun 10 Sep 2023 23:41:15 No.1398339 View View Reply Original Report

Quoted By: >>1398353 >>1398363 >>1398366

How the fuck is sqrt((1+x)/(1-x)) = (sqrt(1-x^2))/(1-x)? Anybody care to help a brainlet?

Anonymous

Anonymous Mon 11 Sep 2023 00:02:43 No.1398353 Report

Quoted By:

>>1398339
>sqrt((1+x)/(1-x)) = (sqrt(1-x^2))/(1-x)

Square both sides:
(1+x)/(1-x) = (1-x^2)/((1-x)^2)

Multiply by (1-x)^2:
(1+x)(1-x) = 1-x^2

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

Anonymous

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Anonymous Mon 11 Sep 2023 00:40:27 No.1398363 Report

Quoted By:

>>1398339
let A = (1+x), B = (1-x)

sqrt(A/B)

sqrt(A) / sqrt(B)

sqrt(A) / sqrt(B) * [sqrt(B) / sqrt(B)]

sqrt(A)*sqrt(B) / [sqrt(B)*sqrt(B)]

sqrt(AB) / B

simple as

Anonymous

Anonymous Mon 11 Sep 2023 01:12:31 No.1398366 Report

Quoted By:

>>1398339
Because multiplication and division are commutative as long as you don’t change the order.

And squaring something is basically just dividing it by it’s square

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