Question

Solve (x-1)^2(x+2)(x-3)/x-2 >0

Answer 1

Absolute Value and Inequalities

Answer 2

\[\frac{(x-1)^{2}(x+2)(x-3)}{(x-2)} > 0\] correct?

Answer 3

\[\frac{(x-1)^{2}(x+2)(x-3)}{(x-2)} > 0\]
If (x-2) is positive then:
\[(x-1)^{2}(x+2)(x-3) > 0\] which is only going to be true for x > 3.

However, if (x-2) is negative then:
\[(x-1)^{2}(x+2)(x-3) < 0\] which is only true when x is between -2 and 2 because \((x-1)^2\) is always positive, \((x+2)\) is positive for x > -2, and \((x-3)\) is negative for all x < 2.

Answer 4

Except for x = 1. There it is also zero.