Question

Given that $x$ is a real number satisfying $\frac{5x^2-26x+5}{3x^2-10x+3}<0$, then

• A. $x<\frac{1}{5}$
• B. $\frac{1}{5}<x<3$
• C. $x>5$
• D. $\frac{1}{5}<x<\frac{1}{3}$ or $3<x<5$

Answer 1

The correct option is D $\frac{1}{5}<x<\frac{1}{3}$ or $3<x<5$

The given inequation is,
$\frac{5x^2-26x+5}{3x^2-10x+3}<0$
Rewrite the above inequation as
$\frac{(x-5)(x-\frac{1}{5})}{(x-3)(x-\frac{1}{3})}<0\Rightarrow x\in (\frac{1}{5},\frac{1}{3})\cup (3,5)$