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

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

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

simplify

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

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

Solution steps

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

Multiply by the conjugate

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

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

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

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

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

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

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

- \frac{1}{4} \cdot \frac{x ^{\frac{3}{4}}}{- 2} \cdot x^{- \frac{1}{4}}

\frac{2}{( x ^{2} - x - 6 )} + \frac{( 3 x )}{( x ^{2} - 9 )}

m^{3} - 14 m + 8

sec^{2} (x) - sin^{2} (x) - cos^{2} (x)

co \frac{tan ( x )}{2}

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