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

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

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simplify (x-1)/(sqrt(x)-1)

simplify

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

x + 1

Solution steps

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

Multiply by the conjugate

\frac{x + 1}{x + 1}

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

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

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

Cancel the common factor:

x - 1

= x + 1

13 - 9

(a - 4) (a + 4)

\frac{2}{3} \times \frac{1}{3}

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

6 x - 8