What is sqrt(1+x)(sqrt(1+x)+sqrt(1-x)) ?

The solution to sqrt(1+x)(sqrt(1+x)+sqrt(1-x)) is 1+x+sqrt(1+x)sqrt(1-x)

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simplify sqrt(1+x)(sqrt(1+x)+sqrt(1-x))

simplify

1 + x (1 + x + 1 - x)

1 + x + 1 + x 1 - x

Solution steps

1 + x (1 + x + 1 - x)

Apply the distributive law:

a (b + c) = ab + a c

1 + x (1 + x + 1 - x) = 1 + x 1 + x + 1 + x 1 - x

= 1 + x 1 + x + 1 + x 1 - x

Apply radical rule:

a a = a,

assuming

a \geq 0

1 + x 1 + x = 1 + x

= 1 + x + 1 + x 1 - x

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

(2 A x + B) e^{x} + e^{x} (A x^{2} + B x + C)

\frac{( x ^{3} + 2 x ^{2} )}{( x + 1 ) ^{2}}

(\frac{5 x + 4}{x ^{2} - 4}) (\frac{4 x + 2}{x ^{2} - 4})

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