solve $\frac{2x+3}{x-5}
2. $\frac{2x+3}{x-5}<\left| \frac{4x+12}{x+1} \right|$ implies that $\frac{4x+12}{x+1}>\frac{2x+3}{x-5}$ or $\frac{4x+12}{x+1}<-\frac{2x+3}{x-5}.$ Do each one of them. Solution set is the union of solution for the first inequality and the second one.
3. thanks i got $\frac{2\sqrt{17}}{4} is this the right answer and what you mean by union? thanks