Solve: `|(x^2-8x+12)/(x^2-10 x+21)|=(-(x^2-8x+12))/(x^2-10 x+21)`

Explanation

The equation has the form `|f(x)|=-f(x)`
when `f(x)=(x^(2)-8x+12)/(x^(2)-10x+21)`
such an equation is equivalent to the collection of systems
`{(c(x)=-f(x),"if"f(x)ge0),(f(x)=f(x),"if"f(x)lt0:}`
The first system is equivalent of `f(x)=0` and the second system is equivalent to `f(x)lt0` the combining both systems, we get
`f(x)le0`
`:.(x^(2)-8x+12)/(x^(2)-10x+21)le0`
`implies((x-2)(x-6))/((x-3)(x-7))le0`

Hence by Wavy curve method,
`x epsilon[2,3)uu[6,7)`