# How do you solve #(x^2-x-2)/(x^2-4x+3)>0#?

##### 1 Answer

Jul 11, 2016

#### Explanation:

So the numerator changes sign at

Each change of sign (numerator or denominator) changes the sign

of the quotient.

So the sign reverses each time we move to the next interval in the sequence:

#(-oo, -1), (-1, 1), (1, 2), (2, 3), (3, oo)#

For large positive values of

So the signs of the quotient in the

#+ - + - +#

So the quotient is positive in

graph{(x^2-x-2)/(x^2-4x+3) [-10, 10, -5, 5]}