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

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

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

simplify

x (x + 1 - x)

x x + 1 - x

Solution steps

x (x + 1 - x)

Apply the distributive law:

a (b - c) = ab - a c

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

= x x + 1 - x x

Apply radical rule:

a a = a,

assuming

a \geq 0

x x = x

= x x + 1 - x

(2 + 3) (6 - 2)

\frac{d}{d θ} ((x (θ)) (θ - sin (θ)))

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

- 2 (4 e^{- x^{2}} x^{3} - 6 e^{- x^{2}} x)

\frac{x + 1}{2 ( x - 1 ) ( 4 x + 1 )}

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