What is (x^3-27)/(x^2-9) ?

The solution to (x^3-27)/(x^2-9) is (x^2+3x+9)/(x+3)

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simplify (x^3-27)/(x^2-9)

simplify

\frac{x ^{3} - 27}{x ^{2} - 9}

\frac{x ^{2} + 3 x + 9}{x + 3}

Solution steps

\frac{x ^{3} - 27}{x ^{2} - 9}

Factor

x^{3} - 27 : (x - 3) (x^{2} + 3 x + 9)

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

Factor

x^{2} - 9 : (x + 3) (x - 3)

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

Cancel the common factor:

x - 3

= \frac{x ^{2} + 3 x + 9}{x + 3}

\frac{x ^{2} + x - 2}{x ^{3} - x ^{2} - x + 1}

49 \div 7

(- 10 - 4 i) - (6 + 9 i)

i^{124}

(n + 6)^{2}