What is (x^2-4x+16)/(x^3+64) ?

The solution to (x^2-4x+16)/(x^3+64) is 1/(x+4)

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simplify (x^2-4x+16)/(x^3+64)

simplify

\frac{x ^{2} - 4 x + 16}{x ^{3} + 64}

\frac{1}{x + 4}

Solution steps

\frac{x ^{2} - 4 x + 16}{x ^{3} + 64}

Factor

x^{3} + 64 : (x + 4) (x^{2} - 4 x + 16)

= \frac{x ^{2} - 4 x + 16}{( x + 4 ) ( x ^{2} - 4 x + 16 )}

Cancel the common factor:

x^{2} - 4 x + 16

= \frac{1}{x + 4}

- 3 \cdot \frac{1}{6}

- 3 \cdot \frac{1}{9}

5 \div \frac{2}{5}

+ 36 1^{\frac{1}{2}}

\frac{9}{6} - \frac{9}{6}