SOLUTION: 42.) Solve each equation. Watch for extraneous solution. 5/y-3 = y+7/2y-6 + 1

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Question 164064This question is from textbook Elementary and Intermediate
: 42.) Solve each equation. Watch for extraneous solution.
5/y-3 = y+7/2y-6 + 1
This question is from textbook Elementary and Intermediate

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

5%2F%28y-3%29+=+%28y%2B7%29%2F%282y-6%29+%2B+1

Write the 1 as 1%2F1 so every term will be
a fraction:

5%2F%28y-3%29+=+%28y%2B7%29%2F%282y-6%29+%2B+1%2F1

Factor 2y-6 by taking out a 2, as 2%28y-3%29

5%2F%28y-3%29+=+%28y%2B7%29%2F%282%28y-3%29%29+%2B+1%2F1

Put every term in parentheses:

%285%2F%28y-3%29%29+=+%28%28y%2B7%29%2F%282%28y-3%29%29%29+%2B+%281%2F1%29

The LCD is 2%28y-3%29.  Put it over 1 and in
parentheses as %28%282%28y-3%29%29%2F1%29 and multiply through by it:



Cancel what will cancel:



All that's left is

2%2A5=y%2B7%2B2%28y-3%29

10=y%2B7%2B2y-6

10=3y%2B1

9=3y

3=y

Check to see if y=3 is a solution:

5%2F%28y-3%29+=+%28y%2B7%29%2F%282y-6%29+%2B+1

5%2F%283-3%29+=+%28y%2B7%29%2F%282%283%29-6%29+%2B+1

5%2F0+=+%28y%2B7%29%2F%286-6%29%2B1

5%2F0+=+%28y%2B7%29%2F0+%2B+1

That contains division by 0 and that is 
always undefined.  So y=3 is not a
solution.  It is call an "extraneous 
solution", and not a genuine solution.
Therefore there is no solution to the
problem.

Edwin