Solve the rational inequality Express your answer using inte

Solve the rational inequality. Express your answer using interval notation. (If there is no solution, enter NO SOLUTION.) x - 9/x + 8lessthanorequalto 0

Solution

(x-9)/(x+8) <=0

First we have to find the critical values and to find it we have to set both numerator and denominator to 0

x-9=0      and     x+8=0

x=9         and        x=-8

So we have three regions here (-infinity,-8), [-8,9),[9,infinity)

In the first region, we get a positive value. Hence this region is not a part of the solution set

In the second region,we get a negative value. Hence it is a part of the solution set

In the third region,we get a positive value. Therefore it is not a part of the solution set

Therefore the solution is

(-8,9]