Question

I'm completely lost on this question please help

Answer 1

first, note that y≠0 and y≠4 because that would make the denomenators 0 which is undefined

 
we got to get rid of fractions
common denomenator is y(y-4)
multiply both sides by y(y-4)
2y+y-4=y(y-1)
3y-4=y²-y
minus 3y both sides
-4=y²-4y
add 4 both sides
0=y²-4y+4
factor
what 2 numbers multiply to get 4 and add to get -4?
-2 and -2
0=(y-2)(y-2)
set to zero

y-2=0
y=2
no extranious roots


y=2 is the solution

Answer 2

Multiply the numerators by "y" which yields:
(2y) / (y-4)  +1 = (y^2 -y) / (y-4)
(2y) / (y-4)  - (y^2 -y) / (y-4) = -1

(2y) - (y^2 -y) / (y-4) = -1

(2y) - (y^2 -y) = -y +1

-y^2 +2y -y +y = 1

-y^2 +2y -1 = 0

Multiplying by -1

y^2 -2y +1 = 0

(y -1) * (y - 1) = 0

x = 1
x= 1