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

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

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simplify (x^2-1)/(sqrt(x)-1)

simplify

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

(x + 1) (x + 1)

Solution steps

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

Multiply by the conjugate

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

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

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

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

Factor

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

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

Cancel the common factor:

x - 1

= (x + 1) (x + 1)

6 + 106

- 4 - 64

(5 a^{- 2})^{2}

\frac{2}{5 + 2}

(m^{5} + 5 n^{4})^{2}

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