Question

$\left\{x \in R: \frac{14 x}{x+1}-\frac{9 x-30}{x-4}<0\right\}$ is equal to

• A. (-1,4)
• B. $(1,4) \cup(5,7)$
• C. (1,7)
• D. $(-1,1) \cup(4,6)$

Answer 1

Answer: (D)

$\left\{x \in R: \frac{14 x}{x+1}-\frac{9 x-30}{x-4}< 0\right\}$
$\frac{14 x(x-4)-(9 x-30)(x+1)}{(x+1)(x-4)}<0$
$\frac{14 x^{2}-56 x-\left(9 x^{2}-30 x+9 x-30\right)}{(x+1)(x-4)}< 0$
$\frac{\left(14 x^{2}-56 x-9 x^{2}+30 x-9 x+30\right)}{(x+1)(x-4)}< 0$
$\frac{\left(5 x^{2}-35 x+30\right)}{(x+1)(x-4)}< 0$
$\frac{\left(x^{2}-7 x+6\right)}{(x+1)(x-4)}< 0, \frac{(x-1)(x-6)}{(x+1)(x-4)}< 0$
Drawn number line,

Hence,
$x \in(-1,1) \cup(4,6)$