SOLUTION: Radical equations: solve 9/(y+3)+2/y = (5y-3)/(y^2-9)

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Question 672733: Radical equations: solve
9/(y+3)+2/y = (5y-3)/(y^2-9)
Answer by radh(108) About Me  (Show Source):
You can put this solution on YOUR website!
Use the difference of squares formula (a^(2)-b^(2)=(a-b)(a+b)) because both terms are perfect squares.
9%2F%28y%2B3%29%2B2%2Fy=%285y-3%29%2F%28%28y-3%29%28y%2B3%29%29

Find the LCD.
y%28y%2B3%29%28y-3%29

Multiply each term in the equation by the LCD in order to remove all the denominators from the equation.
11y%5E%282%29-27y-18=5y%5E%282%29-3y

Move all terms not containing y to the right-hand side of the equation.
6y%5E%282%29-24y-18=0

Factor out the GCF (6).
6%28y%5E%282%29-4y-3%29=0

Divide.
%28y%5E%282%29-4y-3%29=0

Use the quadratic formula to find the solutions.
y=%28-%28-4%29%5C%28sqrt%28-4%29%29%5E%282%29-4%281%29%28-3%29%29%29%2F%282%281%29%29
The final answer is the combination of both solutions.
y=2%2B%28sqrt%287%29%29%2C2-%7E%287%29

Hope this helps!