ABC26GN1223 · Simplification

$\frac{x^{2}-1}{x}=4 \Rightarrow\left(\frac{x^{2}-1}{x}\right)^{3}=4^{3}=64$ $$\begin{aligned} & \Rightarrow \frac{x^{6}-1-3 x^{2}\left(x^{2}-1\right)}{x^{3}}=64 \\ & \Rightarrow \frac{x^{6}-1-3 x^{2} \cdot 4 x}{x^{3}}=64 \\ & \Rightarrow x^{6}-1-12 x^{3}=64 x^{3} \\ & \Rightarrow x^{6}-1=76 x^{3} \Rightarrow \frac{x^{6}-1}{x^{3}}=76 \end{aligned}$$