SOLUTION: Solve the equation and atate any extraneous solutions. Thanks! 2y/ y - 4 - 3/ 5 = 3

Algebra ->  Equations -> SOLUTION: Solve the equation and atate any extraneous solutions. Thanks! 2y/ y - 4 - 3/ 5 = 3      Log On


   

Question 35539: Solve the equation and atate any extraneous solutions. Thanks!
2y/ y - 4 - 3/ 5 = 3
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
%282y%29%2F%28+y+-+4%29+-+3%2F+5+=+3

Start by adding 3%2F5 to each side of the equation:
%282y%29%2F%28+y+-+4%29++=+3%2B3%2F5+
%282y%29%2F%28+y+-+4%29++=+18%2F5+

Now, since a%2Fb=c%2Fd means the same as a%2Ad=b%2Ac, it follows that
%282y%29%2F%28+y+-+4%29++=+18%2F5+ means that 10y+=+18%28y-4%29+

So, 10y+=+18y+-+72
-8y+=+-72
y=+9

This value of y does NOT make any denominators zero, so there are no extraneous roots. However, it's easy to check by substituting y=9 in the original equation:
%282y%29%2F%28+y+-+4%29+-+3%2F+5+=+3
%282%2A9%29%2F%28+9+-+4%29+-+3%2F+5+=+3
18%2F5+-+3%2F5+=+3
15%2F5+=+3

It checks!!

R^2 at SCC