Question 1199000
<br>
Given the answer choices, by far the quickest path to the answer is to see which one works.  From the given answer choices, the x values -1, 7, and 8 need to be the endpoints of the solution interval(s) -- which means the value of the expression is either 0 or undefined at those values.<br>
The expression is undefined at x=-1 and 0 at x=7; it is neither 0 nor undefined at x=8.  Since the inequality is a strict inequality (endpoints of the intervals not included), the solution set is either (-1,7) or (-infinity,-1) U (7,infinity).  But that second possibility is not one of the answer choices, so<br>
ANSWER: A) (-1,7)<br>
But surely the intended purpose of the problem was for you to learn how to get that answer....<br>
Keep everything on one side of the inequality, with "0" on the other side; and combine the terms on the left with a common denominator so the expression is a rational function.<br>
{{{(x+9)/(x+1) -2 > 0}}}<br>
{{{(x+9)/(x+1)-(2(x+1))/(x+1) > 0}}}<br>
{{{(x+9-2x-2)/(x+1) > 0}}}<br>
{{{(-x+7)/(x+1) > 0}}}<br>
That rational function is equal to 0 at x = 7 and is undefined at x = -1, so those are endpoints of the interval(s) of the solution set.  And evaluating the expression at x = 0 shows the inequality is satisfied, so the solution set is (-1,7).<br>