Solve each rational inequality and express the solution set in interval notation. $$\frac{2}{x-5}-\frac{1}{x-1} \geq 0$$
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Step 1
$$\frac{2}{x-5}-\frac{1}{x-1} = 0$$ $$\frac{2(x-1) - (x-5)}{(x-5)(x-1)} = 0$$ $$\frac{2x-2-x+5}{(x-5)(x-1)} = 0$$ $$\frac{x+3}{(x-5)(x-1)} = 0$$ Critical points: $x=-3, 1, 5$ Vertical asymptotes: $x=1, 5$ ** Show more…
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