107k views
4 votes
Solve (1)/(x+1)+(1)/(x-3)<0. Write your solution using interval notation.

User Wallybh
by
7.6k points

1 Answer

4 votes

Final answer:

To solve the inequality (1)/(x+1)+(1)/(x-3)<0, find the values of x for which the expression is negative, considering the critical points x=-1 and x=3. The solution in interval notation is (-1, 3), as this is the interval where the expression is negative but not undefined.

Step-by-step explanation:

To solve the inequality (1)/(x+1)+(1)/(x-3)<0, we must find the values of x for which the expression is negative. We can consider the critical points, which are where the expression is undefined or equal to zero. These points are at x=-1 and x=3. We can test the intervals created by these critical points to determine where the expression is negative.

First, we analyze the sign of each fraction in the intervals (-∞, -1), (-1, 3), and (3, ∞). The sign of the first fraction changes at x=-1 and that of the second fraction changes at x=3. By testing values from each interval, we find that the expression is negative in the interval (-1, 3).

In interval notation, the solution is (-1, 3). We must exclude the points x=-1 and x=3 because at these points the expression is undefined.

User ArisRS
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories