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

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

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

simplify

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

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

Solution steps

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

Factor

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

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

Factor

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

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

Cancel the common factor:

y + 3

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

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

x^{3} \cdot x^{8}

\frac{5}{4} \cdot \frac{3}{7}

\frac{5}{x - 5} - \frac{5}{x + 5}