Answer
a. See graph. $-1\lt x\lt 1$ or $ x\lt-5$
b. See proof below.
Work Step by Step
a. See the graph. $\frac{3}{x-1}\lt \frac{2}{x+1}$ happens when $-1\lt x\lt 1$ or $ x\lt-5$
b. To satisfy $\frac{3}{x-1}\lt \frac{2}{x+1}$
When $-1\lt x\lt 1$
$(x-1)(x+1)\lt0$
We have $3x+3\gt 2x-2$
This gives $ x\gt-5$
So the condition for this case is $-1\lt x\lt 1$
When $ x\lt-1$ or $ x\gt 1$:
$(x-1)(x+1)\gt0$
We have $3x+3\lt 2x-2$
This gives $ x\lt-5$,
So the condition for this case is $ x\lt-5$
