SOLUTION: Hello! My name is Salem and I am a concurrently enrolled student at Carl Albert State College. I have just started College Algebra and I asked my high school math teacher to help m

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Question 84323This question is from textbook College Algebra
: Hello! My name is Salem and I am a concurrently enrolled student at Carl Albert State College. I have just started College Algebra and I asked my high school math teacher to help me with this question and neither of us can get it right. Can you please help me? It is due tomorrow!
Here is the question:
%28x%2Fx%5E2-1%29-%28%28x%2B3%29%2Fx%5E2-x%29=%28%28-3%29%2Fx%5E2%2Bx%29
In words, it is: (x over x squared minus one), minus (x plus three over x squared minus x) equals (negative three over x squared plus x). This question is from textbook College Algebra

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F%28x%5E2-1%29+-+%28%28x%2B3%29%2F%28x%5E2+-+x%29%29+=+%28-3%29%2F%28x%5E2+%2Bx%29+

First factor each denominator in order to find the LCD:


The LCD = x(x-1)(x+1), so multiply both sides of the equation by the LCD, makin note that x cannot equal 0, 1, or -1:


When ALL these denominators divide out, this is all that is left:
x%5E2+-%28x%2B1%29%28x%2B3%29+=+%28x-1%29%28-3%29+
x%5E2+-%28x%5E2+%2B4x%2B3%29+=+-3x%2B3
x%5E2+-x%5E2+-4x-3+=+-3x+%2B3+
-4x-3=-3x%2B3
-4x%2B3x-3+=+-3x%2B3x%2B3
-x-3%2B3=3%2B3
-x=6
x=-6

The answer does NOT make any denominators zero, so it should check okay!
It does, but it's hairy!

R^2 at SCC

PS. Get your math teacher to check out my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Take a look at, among other pages, my "MATH IN LIVING COLOR PAGES!"