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

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

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

simplify

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

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

Solution steps

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

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

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

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

Simplify

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

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

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

(1 - cos (2 x)) (1 - cos (2 x)) (1 - cos (2 x))

f (x - 10) (x + 10) d x

(a + 5)^{2}

(sec (x) + tan (x) - 1) (sec (- tan (x) + 1))

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