Question 314409
First, factor the third denominator into x(x+1).  Then realize that the LCD is  x(x+1).  Now, multiply both sides of the equation by x(x+1).


{{{x(x+1)*(1/x) + x(x+1)*(1/(1+x)) = x*(x+1)*((-3)/(x(x+1)))}}}

{{{x+1 + x = -3}}}
{{{2x=-4}}}
{{{x=-2}}}


Finally, check each denominator to make sure that when x=-2, no denominators are equal to zero.


For additional help with these topics, please see my OWN website by clicking on my tutor name "rapaljer" anywhere in algebra.com.  Click on my website which is given there, and look on my Homepage for the link "Basic, Intermediate, and College Algebra: One Step at a Time."  Select "Intermediate Algebra", and look in "Chapter 3" for "3.05 Fractional Equations".  In addition to a detailed explanation, with examples, exercises, and ALL the answers, many of the exercises are solved IN COLOR on the "Math in Living Color" pages that go with this section.


Also, I have a video called "Fractional and Literal Equations" that was made a few years ago in one of my classrooms, that can be viewed from my website FREE.  To see the videos look on my Homepage for the link "Rapalje Videos in Living Color."  Choose "Intermediate Algebra".  Let me know if they help, or if you have questions--my Email address is at the bottom of each page of my website.  Math is usually not as hard as it looks!!


Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus