SOLUTION: I have a few questions like these in my college algebra book with no examples to help. 10-13/x=4+5/x and x/(x+4) + 4/(x+4) + 2= 0

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Question 153428: I have a few questions like these in my college algebra book with no examples to help.
10-13/x=4+5/x
and
x/(x+4) + 4/(x+4) + 2= 0
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
10-13%2Fx+=+4+%2B+5%2Fx Multiply both sides by x.
10x-13+=+4x%2B5 Subtract 4x from both sides.
6x-13+=+5 Add 13 to both sides.
6x+=+18 Finally, divide both sides by 6.
x+=+3
---------------
x%2F%28x%2B4%29+%2B+4%2F%28x%2B4%29+%2B+2+=+0 Multiply through by (x+4)
x%2B4%2B2%28x%2B4%29+=+0 Expand the last term.
x%2B4%2B2x%2B8+=+0 Combine like-terms.
3x%2B12+=+0 Subtact 12 from both sides.
3x+=+-12 Finally, divide both sides by 3.
x+=+-4
The only problem with this solution is that it is x = -4 is an excluded value.
Why? Because, when you substitute x = -4 into the original equation, the first two terms are undefined:
-4%2F%28-4%2B4%29+%2B+4%2F%28-4%2B4%29+%2B+2+=+0
%28-4%29%2F0+%2B+4%2F0+%2B+2+=+0 As you can see, the first two terms are undefined because division by zero is not defined.