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 A (-1,4)

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

$x+1\ne 0$ $x-4\ne 0$

$\Rightarrow x\ne -1$ $x\ne 4$

$14(x-4)-(x+1)(7x-30)<0$

$14x^2-56x-(9x^2-30x+9x-30)<0$

$14x^2-56x-9x^2+30x-9x+30<0$

$5x^2-35x+30<0$

$x^2-7x+6<0$

$x^2-6x+6<0$

$x(x-6)-1(x-6)<0$

$(x-1)(x-6)<0$

$\Rightarrow x>1$ & $x<6$

$\Rightarrow xϵ;(1,4)\cup (4,6)$