SOLUTION: solve the equation for y (5/y-3)+ (10/y^2-y-6) = (y/y+2)] (five over y-3) plus (10 over y squared minus y minus 6) equals (y over y+2) 1.Im not sure if i did it right, i f

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: solve the equation for y (5/y-3)+ (10/y^2-y-6) = (y/y+2)] (five over y-3) plus (10 over y squared minus y minus 6) equals (y over y+2) 1.Im not sure if i did it right, i f      Log On


   

Question 572842: solve the equation for y
(5/y-3)+ (10/y^2-y-6) = (y/y+2)]
(five over y-3) plus (10 over y squared minus y minus 6) equals (y over y+2)
1.Im not sure if i did it right, i found the least common denominator which is (y-3)(y+2) and multiplied to the missing part of the least common denominator to the top to get:
5(y+2)/(y-3)(y+2) - 10/(y-3)(y+2) = y(y-3)/(y+2)(y-3)
2.Then i combined like terms and simplified to get
5y+20/(y-3)(y+2) = (y^2)-3y/(y+2)(y-3)
3. My final answer was
5y(y+4)/ (y+2)(y-3)
Is it correct?

Found 2 solutions by solver91311, mananth:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


You were correct up to this point:



But , so the next step looks like:



Then multiply both sides by the denominator to eliminate the denominator leaving you with:



Which becomes



hence



or



Check to be certain that neither root will drive any original denominator to zero before declaring either an element of the solution set. You might want to check the work by substituting back into the original equation.

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
%285%2F%28y-3%29%29%2B+%2810%2F%28y%5E2-y-6%29%29+=+%28y%2F%28y%2B2%29%29
%285%2F%28y-3%29%29%2B+%2810%2F%28%28y-3%29%28y%2B2%29%29%29+=+%28y%2F%28y%2B2%29%29
Multiply by (y-3)(y+2)
5(y+2) +10 =y(y-3)
5y+10+10=y^2-3y
5y+20=y^2-3y
y^2-8y-20=0
y^2-10y+2y-20=0
y(y-10)+2(y-10)=0
(y-10)(y+2)=0
y=10 OR -2