Solve the rational inequality?

x-6

_____ >0

x+1

Find the zeroes of the numerator and denominator: this is where sign changes will occur:

------(-1)--------(6)-------

Test the three regions for positive results: ( >0 means only positives)

If x< -1, like x= -4, both numerator and denominator will be negative, which makes the fraction positive.

So x< -1

Then if x is between -1 and 6, like x= 0, we will get (-)/(+) which is negative . So this is not part of the solution.

Then x> 6 will give (+)/(+) so this is part of the solution.

X>6

Solution: x<-1 OR x>6

(It' s not hard to do, just trying numbers in each interval:)

I hope this helps!