Find all real numbers that satisfy the equation: \(\frac{1}{r^3+7}-7=\frac{-r^3}{r^3+7}\).
\(\frac{1}{r^3+7}-7=\frac{-r^3}{r^3+7}\\ \frac{1}{r^3+7}-\frac{-r^3}{r^3+7}=7\\ \frac{1+r^3}{r^3+7}=7\\ 1+r^3=7r^3+49\\ 6r^3=-48\\ r^3=-8\\ r=\boxed{-2} \)
I hope this helped,
Gavin