Question

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

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

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