SOLUTION: I am getting confused to do this question please help me to solve this. Hoping for your cooperation. 1. Solve:- a. y-1/y+1=2y-3/2y+3 b. 2/y-1+3/y+1=5/y

Question 970613: I am getting confused to do this question please help me to solve this. Hoping for your cooperation.
1. Solve:-
a. y-1/y+1=2y-3/2y+3
b. 2/y-1+3/y+1=5/y
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
first one:

(y-1)/(y+1) = (2y-3) / (2y+3)

cross multiply to get (y-1) * (2y+3) = (y+1) * (2y-3)

simplify to get 2y^2 + 3y - 2y - 3 = 2y^2 -3y + 2y - 3

combine like terms to get 2y^2 + y - 3 = 2y^2 - y - 3

subtract 2y^2 from both sides of the equation and add y to both sides of the equation and add 3 to both sides of the equation to get:

2y^2 - 2y^2 + y + y -3 + 3 = 2y^2 - 2y^2 - y + y - 3 + 3

combine like terms to get:

2y = 0

divide both sides of the equation by 2 to get y = 0

that's your solution for the first one.

second one:

2/(y-1) + 3/(y+1) = (5/y)

multiply both sides of the equation by y*(y-1)*(y+1) to get:

2/(y-1)*y*(y-1)*(y+1) + 3/(y+1)*y*(y-1)*(y+1) = (5/y)*y*(y-1)*(y+1)

simplify to get:

2*y*(y+1) + 3*y*(y-1) = 5*(y-1)*(y+1)

simplify to get:

2y^2 + 2y + 3y^2 - 3y = 5y^2 - 5

combine like terms to get:

5y^2 - y = 5y^2 - 5

subtract 5y^2 from both sides of the equation to get:

5y^2 - 5y^2 - y = 5y^2 - 5y^2 - 5

combine like terms to get:

-y = -5

solve for y to get y = 5.

that's your solution for the second one.

-----

solution for the first one is y = 0
solution for the second one is y = 5

confirm by replacing y in the respective equations by the value for y in that eqution to see if the equations are true.

(y-1)/ (y+1) = (2y-3) / (2y+3) becomes:

-1 / 1 = -3 / 3 which becomes:

-1 = -1

first equation is true so the folution for the first problem is good.

2 / (y-1) + 3 / (y+1) = 5 / y becomes:

2 / 4 + 3 / 6 = 5 / 5

2/4 = 1/2 and 3/6 = 1/2 and 5/5 = 1, so you get:

1/2 + 1/2 = 1 which is true so the solution for the second problem is also good.

your solution to the first problem is y = 0.
your solution to the second problem is y = 5.

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