how you do?

Solve for x:
(x^3-7)/(x+5) = 0

Multiply both sides by x+5:
x^3-7 = 0

Add 7 to both sides:
x^3 = 7

Taking cube roots gives 7^(1/3) times the third roots of unity:
Answer: |  x = -(-7)^(1/3)       or       x = 7^(1/3)      or        x = (-1)^(2/3) 7^(1/3)

Using polynomial division

\(\frac{x^3-7}{x+5}= x^2-5x+25-\frac{32}{x+5}\)