how to solve: ((x+1)(x-3))/(x-2)^2>0

Question

 it is a question related to inequalities

 

Answer 1

look at the denominator; it's always > 0 unless x = 2, which is excluded from the domain.

 

therefore the sign of the entire expression depends on the behavior of x; its zeros divide the real number line into three intervals.  just test for values WITHIN intervals (-infinity,-1)  (-1,3) and (3,infinity).

 

That is, just select values such as -2, 0 and 4 (and no others) to determine the SIGN of each of the two factors in the numerator.  Just show your work in an orderly manner.  For example, in the leftmost interval mentioned, both factors are positive so all numbers therein are part of the solution.  And in (-1,3) EXCEPT for 2, which was ruled out previously, the product is always negative.  I will let you finish the job nicely...normally the answer is stated as the union of various subintervals.