What is (x^2-81)/(sqrt(x)-3) ?

The solution to (x^2-81)/(sqrt(x)-3) is (x+9)(sqrt(x)+3)

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simplify (x^2-81)/(sqrt(x)-3)

simplify

\frac{x ^{2} - 81}{x - 3}

(x + 9) (x + 3)

Solution steps

\frac{x ^{2} - 81}{x - 3}

Multiply by the conjugate

\frac{x + 3}{x + 3}

= \frac{( x ^{2} - 81 ) ( x + 3 )}{( x - 3 ) ( x + 3 )}

(x - 3) (x + 3) = x - 9

= \frac{( x ^{2} - 81 ) ( x + 3 )}{x - 9}

Factor

x^{2} - 81 : (x + 9) (x - 9)

= \frac{( x + 9 ) ( x - 9 ) ( x + 3 )}{x - 9}

Cancel the common factor:

x - 9

= (x + 9) (x + 3)

\frac{16}{9} + 1

\frac{5}{4} - \frac{3}{5}

\frac{6 ^{2}}{6 ^{4}}

(4 + 7) (8 - 7)

16 x - 12

What is (x^2-81)/(sqrt(x)-3) ?
The solution to (x^2-81)/(sqrt(x)-3) is (x+9)(sqrt(x)+3)