SOLUTION: Hi could you help me solve this rational equation? y-3/5 = y+1/7 thanks

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Question 136242: Hi could you help me solve this rational equation?
y-3/5 = y+1/7
thanks
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
I have to assume that you meant: %28y-3%29%2F5=%28y%2B1%29%2F7, because what you wrote: y-3%2F5=y%2B1%2F7 has no solution.

%28y-3%29%2F5=%28y%2B1%29%2F7

7 and 5 have no common factors so the LCD is 7*5=35, so:
7%28y-3%29%2F35=5%28y%2B1%29%2F35

Add the additive inverse of the right side to both sides:
7%28y-3%29%2F35-5%28y%2B1%29%2F35=0

Since both fractions have the same denominator, add the numerators directly:
%287%28y-3%29-5%28y%2B1%29%29%2F35=0

Distribute and collect like terms:
%282y-26%29%2F35=0

We know that a%2Fb=0 if and only if a=0 and b%3C%3E0. The denominator is not a problem because clearly 35%3C%3E0, so all we need do is set the numerator equal to zero and solve:
2y-26=0
2y=26
y=13

Check:
%2813-3%29%2F5=%2813%2B1%29%2F7
10%2F5=14%2F7
2=2, Answer checks.