Can someone please help me a.s.a.p? The solutions toMy answer options are: a.(-infinity,5)U(1,infinity) b.(-infinity,-5)U(-2,1) c.(-5,-2)U(1,5) d.(-2,1)U(5,infinity) I thought the answer was b., what do you think? Thanks Get LCD on the left: To find the critical values, set each factor of the numerator and the denominator = 0, and solve for x: yields critical value x = -5 yields critical value x = -2 yields critical value x = 1 Mark the critical values on a number line: -------o--------o--------o------ -7 -6 -5 -4 -3 -2 -1 0 1 2 3 Pick any value left of -5, say -6. Substitute it into: That is true, so shade the part of the number line to the left of -5. <======o--------o--------o------ -7 -6 -5 -4 -3 -2 -1 0 1 2 3 Next, pick any value between of -5 and -2, say -3. Substitute it into: That is false, so do not shade the part of the number line between -5 and -3, so we still have: <======o--------o--------o------ -7 -6 -5 -4 -3 -2 -1 0 1 2 3 Pick any value between -2 and 1, say 0. Substitute it into: That is true, so shade the part of the number line between -2 and 1. <======o--------o========o------ -7 -6 -5 -4 -3 -2 -1 0 1 2 3 Pick any value right of 1, say 2. Substitute it into: That is false, so do not shade the part of the number line to the right of 1. So far the number line so far gives: <======o--------o========o------ -7 -6 -5 -4 -3 -2 -1 0 1 2 3 We are technically supposed to test the critical values themselves to see if they are solutions. But none do since substituting -5 or -1 for x gives 0 > 0, and substituting 1 for x causes the left side to be undefined. So that number line is represented by this interval notation: (-oo,-5) U (-2,1) So you are correct since that's choice b. Edwin