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

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

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

expand

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

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

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

a = (1 + \frac{x ^{2}}{1 - x ^{2}}), b = 1, c = 1 - x^{2}

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

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

Simplify

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

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

(e^{4 x}) (x^{2} \frac{d y}{d x} + 2 x y)

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

\frac{d}{d t} ((a (t)) (a (t)^{4} + t^{4} - 6 a (t)^{2} t))

\frac{j + 2}{( - 2 + j ) ( j - 1 ) ( j ^{2} + 2 j + 5 )}

s q r 1 + \frac{1}{( 9 x ^{\frac{4}{3}} )}

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