Question

find the range of x if [{(x-2)(x-4)(x-7)}/{(x+2)(x+4)(x+7)}]>1

Answer 1

\[\frac{(x-2)(x-4)(x-7)}{(x+2)(x+4)(x+7)}>1\]
\[\frac{(x-2)(x-4)(x-7)-(x+2)(x+4)(x+7)}{(x+2)(x+4)(x+7)}>0\]
\[\frac{-2(13x^2+56)}{(x+2)(x+4)(x+7)}>0\]
\[\frac{13x^2+56}{(x+2)(x+4)(x+7)}<0\]
\[x\in(-\infty,-7)\cup (-4,-2)\]