Solve for x
x\in (-\infty,-\frac{1}{4}]\cup (1,\infty)
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-4x-1\leq 0 1-x<0
For the quotient to be ≥0, -4x-1 and 1-x have to be both ≤0 or both ≥0, and 1-x cannot be zero. Consider the case when -4x-1\leq 0 and 1-x is negative.
x>1
The solution satisfying both inequalities is x>1.
-4x-1\geq 0 1-x>0
Consider the case when -4x-1\geq 0 and 1-x is positive.
x\leq -\frac{1}{4}
The solution satisfying both inequalities is x\leq -\frac{1}{4}.
x>1\text{; }x\leq -\frac{1}{4}
The final solution is the union of the obtained solutions.
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