SOLUTION: solve and check: 3/y= 1/2 + 1/2y I have no clue where to begin for this problem, please help thank you!

Question 414408: solve and check:
3/y= 1/2 + 1/2y
I have no clue where to begin for this problem, please help thank you!
Answer by woolybear(13) (Show Source): You can put this solution on YOUR website!
(3)/(y)=(1)/(2)+(1)/(2)*y
Multiply (1)/(2) by y to get (y)/(2).
(3)/(y)=(1)/(2)+(y)/(2)
Combine the numerators of all expressions that have common denominators.
(3)/(y)=(y+1)/(2)
Since there is one rational expression on each side of the equation, this can be solved as a ratio. For example, (A)/(B)=(C)/(D) is equivalent to A*D=B*C.
3*2=(y+1)*y
Since y is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
(y+1)*y=3*2
Multiply (y+1) by y to get y(y+1).
y(y+1)=3*2
Multiply 3 by 2 to get 6.
y(y+1)=6
Multiply y by each term inside the parentheses.
y^(2)+y=6
To set the left-hand side of the equation equal to 0, move all the expressions to the left-hand side.
y^(2)+y-6=0
In this problem 3*-2=-6 and 3-2=1, so insert 3 as the right hand term of one factor and -2 as the right-hand term of the other factor.
(y+3)(y-2)=0
Set each of the factors of the left-hand side of the equation equal to 0.
y+3=0_y-2=0
Since 3 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 3 from both sides.
y=-3_y-2=0
Set each of the factors of the left-hand side of the equation equal to 0.
y=-3_y-2=0
Since -2 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 2 to both sides.
y=-3_y=2
The complete solution is the set of the individual solutions.
y=-3,2
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