Find all real values of x such that \(\frac{x^2 + x + 3}{2x^2 + x - 6} \ge 0.\)
The solution can be written in multiple ways. Find the best way that you need.
\begin{bmatrix}\mathrm{Solution:}\:&\:x<-2\quad \mathrm{or}\quad \:x>\frac{3}{2}\:\\ \:\mathrm{Decimal:}&\:x<-2\quad \mathrm{or}\quad \:x>1.5\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-2\right)\cup \left(\frac{3}{2},\:\infty \:\right)\end{bmatrix}
Ok.
So if u take the equation and then factor the equation u should get
x^2+x+3/(2x-3)(x+2)
Once you get that then find the intervals:
Look at the circled numbers and those are the intervals (or you can all them the answers) and then the answer I wrote previously was ways you can write it!!
Hope this helped!!