What is ((sqrt(x^2+1)-x))/((sqrt(x^2+1)+x)) ?

The solution to ((sqrt(x^2+1)-x))/((sqrt(x^2+1)+x)) is (sqrt(x^2+1)-x)^2

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simplify ((sqrt(x^2+1)-x))/((sqrt(x^2+1)+x))

simplify

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

(x^{2} + 1 - x)^{2}

Solution steps

\frac{x ^{2} + 1 - x}{x ^{2} + 1 + x}

Multiply by the conjugate

\frac{x ^{2} + 1 - x}{x ^{2} + 1 - x}

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

Simplify

(x^{2} + 1 - x) (x^{2} + 1 - x) : (x^{2} + 1 - x)^{2}

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

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

Apply rule

\frac{a}{1} = a

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

(4 \cdot 3) (2 x^{3})

3 x^{2} + 75 y^{2}

\frac{( a ^{\frac{1}{5}} \cdot a ^{\frac{2}{3}} )}{( a ^{\frac{3}{5}} )}

\frac{( a ^{2} + 1 )}{( 1 + \frac{1}{a ^{2}} )}

v (2.2) f (- 1.2)

What is ((sqrt(x^2+1)-x))/((sqrt(x^2+1)+x)) ?
The solution to ((sqrt(x^2+1)-x))/((sqrt(x^2+1)+x)) is (sqrt(x^2+1)-x)^2