Question

{$xϵR:\frac{14x}{x+1}-\frac{9x-30}{x-4}<0$ } is equal to

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

Answer 1

The correct option is D $(-1,1)\cup (4,6)$

Given,

$\frac{14x}{x+1}-\frac{9x-30}{x-4}<0$

$\frac{5x^2-35x+30}{(x+1)(x-4)}<0$

$\frac{(x-1)(x-6)}{(x+1)(x-4)}<0$

For $(x-1),(x-6)$ and $(x+1),(x-4)$ we get,

$-1<x<1or4<x<6$

$\left[\begin{array}{cc}Solution:& -1<x<1or4<x<6\\ IntervalNotation:& (-1,1)\cup (4,6)\end{array}\right]$