Simplify-1-x-x-1-x-x-

Question Number 168054 by Mastermind last updated on 01/Apr/22

S i m p l i f y \frac{\sqrt{1 + x} + \sqrt{x}}{\sqrt{1 - x} + \sqrt{x}}

Commented by MJS_new last updated on 01/Apr/22

what do you want ? what is “ {simple}^{″} ?

we can do this :

\frac{\sqrt{1 + x} + \sqrt{x}}{\sqrt{1 - x} + \sqrt{x}} = \frac{\sqrt{1 + x} + \sqrt{x}}{\sqrt{1 - x} + \sqrt{x}} \times \frac{\sqrt{1 - x} - \sqrt{x}}{\sqrt{1 - x} - \sqrt{x}} =

= \frac{\sqrt{1 - x^{2}} + (\sqrt{1 - x} - \sqrt{1 + x}) \sqrt{x} - x}{1 - 2 x}

but is this “ {simplified}^{″} ?

Commented by Mastermind last updated on 02/Apr/22

Y o u d i d a g r e a t j o b, T h a n k s s o m u c h

Commented by Mastermind last updated on 02/Apr/22

T h a n k s t o e v e r y o n e

Answered by HeferH last updated on 01/Apr/22

\frac{\sqrt{1 + x} + \sqrt{x}}{\sqrt{1 - x} + \sqrt{x}} \cdot \frac{\sqrt{1 - x} - \sqrt{x}}{\sqrt{1 - x} - \sqrt{x}} \Rightarrow

\frac{{(\sqrt{1 + x})}^{2} - {(\sqrt{x})}^{2}}{{(\sqrt{1 - x})}^{2} - {(\sqrt{x})}^{2}} = \frac{1 + x - x}{1 - x - x} = \frac{1}{1 - 2 x}

Commented by MJS_new last updated on 01/Apr/22

wrong .

(\sqrt{1 + x} + \sqrt{x}) (\sqrt{1 - x} + \sqrt{x}) \neq {(\sqrt{1 + x})}^{2} - {(\sqrt{x})}^{2}

Commented by HeferH last updated on 01/Apr/22

y e a h, I m a d e a m i s t a k e, s o r r y

({d i d n}^{'} t r e a l i z e)

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