What is (x^4-16)/(x^3-8) ?

The solution to (x^4-16)/(x^3-8) is ((x^2+4)(x+2))/(x^2+2x+4)

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simplify (x^4-16)/(x^3-8)

simplify

\frac{x ^{4} - 16}{x ^{3} - 8}

\frac{( x ^{2} + 4 ) ( x + 2 )}{x ^{2} + 2 x + 4}

Solution steps

\frac{x ^{4} - 16}{x ^{3} - 8}

Factor

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

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

Factor

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

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

Cancel the common factor:

x - 2

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

\frac{9 x}{8} - \frac{8 x}{5}

∣ 1 + i ∣^{2}

2 x + x - 1

\frac{1}{5} - \frac{3}{2}

What is (x^4-16)/(x^3-8) ?
The solution to (x^4-16)/(x^3-8) is ((x^2+4)(x+2))/(x^2+2x+4)