SOLUTION: 5/y-3=y+7/2y-6+1 I need help solving this

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Question 173560: 5/y-3=y+7/2y-6+1 I need help solving this
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
5/y-3=y+7/2y-6+1

Hmmm! You didn't put parentheses to show where numerators 
and denominators begin "(" and end ")", so I'm guessing you
mean one of two possibilities.  I'll do both:

If you mean this:



Write the  as  so every term will
be a fraction:



Enclose each term in parentheses:



Factor the denominator  as 



Find the LCD, which is , which we will
write as  and multiply each term
by it:



Cancel what will cancel:



All that's left is:



Distribute:



Combine like terms:



Add -1 to both sides



Divide both sides by 3:



Now we must check this answer, by
substituting it into the original, to make sure it
is not an extraneous solution:









But since division by 0 is undefined, there is
no solution. 3 was an extraneous, or "bogus"
solution, not an actual solution.

================

If you meant this:



Use 1 denominators so that all terms will be
fractions:



Enclose each term in parentheses:



Factor the denominator  as 



Find the LCD, which is , which we will
write as  and multiply each term
by it:



Cancel what will cancel:



All that's left is:





Distribute to remove parentheses:



Collect like terms:



Get 0 on the left by subtracting 10 from both sides:



or, since I like to have 0 on the right, not left,
I'll switch the sides:




That doesn't factor, so we use the quadratic
formula:













Factor 2 out of the numerator:



Cancel the 2 on top into the 4 on the bottom,
getting 2 on the bottom:





This is difficult to check. However if we were
to substitute that in the original, none of the
denominators would be 0, as they were in the
first way I assumed you meant.  So these are both
solutions.

Edwin


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