Question

Solve the following inequality and write your answer using interval notation.
(x+1 / x^4-x^3+64x-64 )≥ 0

Answer 1

\[\frac{x+1}{x^4-x^3+64x-64}\geq 0\]\[\frac{x+1}{x^3(x-1)+64(x-1)}\geq 0\]\[\frac{x+1}{(x-1)(x^3+64)}\geq 0\]\[\frac{x+1}{(x-1)(x+4)(x^2-4x+16)}\geq 0\]\[\frac{x+1}{(x-1)(x+4)((x-2)^2+12)}\geq 0\]\[x\in(-4,-1]\cup(1,+\infty)\]