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

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

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simplify (z^2-9)/(z^3+27)

simplify

\frac{z ^{2} - 9}{z ^{3} + 27}

\frac{z - 3}{z ^{2} - 3 z + 9}

Solution steps

\frac{z ^{2} - 9}{z ^{3} + 27}

Factor

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

= \frac{( z + 3 ) ( z - 3 )}{z ^{3} + 27}

Factor

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

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

Cancel the common factor:

z + 3

= \frac{z - 3}{z ^{2} - 3 z + 9}

14 - (- 2)

12 x^{2} + 22 x - 20

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9 (4 f - 4 g + 6)

(x - 3)^{2} + 8 (x - 3) + 4