What is ((2x-1))/((sqrt(x-1)+\sqrt{x))} ?

The solution to ((2x-1))/((sqrt(x-1)+\sqrt{x))} is -(2x-1)(sqrt(x-1)-sqrt(x))

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simplify ((2x-1))/((sqrt(x-1)+\sqrt{x))}

simplify

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

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

Solution steps

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

Multiply by the conjugate

\frac{x - 1 - x}{x - 1 - x}

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

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

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

Apply the fraction rule:

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

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

Apply rule

\frac{a}{1} = a

= - (2 x - 1) (- x + x - 1)

(3 a + 2 b - 1)^{3}

\frac{1}{2 ( 6 e - 3 f - \frac{3}{4} )}

(x^{4} - x^{3} + x^{2} - x + 1) + (x + x^{4} - 1 - x^{2})

6 x^{2} - 4 a

(1 + w)^{3}

What is ((2x-1))/((sqrt(x-1)+\sqrt{x))} ?
The solution to ((2x-1))/((sqrt(x-1)+\sqrt{x))} is -(2x-1)(sqrt(x-1)-sqrt(x))