solve for y?

Question

2/y=3/y+2+1

to clara montez
it cant be to easy if you it wrong huh?
the answer you said is none of the choices!

Answer 1

Please use parentheses. I'm going to assume that this is the problem you meant.
2/y = 3/(y+2) + 1
Start by multiply everything by y(y+2)
y(y+2)(2/y) = y(y+2)(3/(y+2)) + y(y+2)(1)
Cancel a few things and you are left with
(y+2)(2) = y(3) + y(y+2)
Multiply everything out.
2y + 4 = 3y + y^2 + 2y
Combine like terms on the right side
2y + 4= y^2 + 5y
Move everything to the right side by subtracting 2y and subtracting 4
0 = y^2 + 3y - 4
Factor the right side
What factors of -4 add to 3?
4 times -1 equals -4 and 4 plus -1 equals 3.
0 = (y+4)(y-1)
Set each part equal to zero.
y+4 = 0 or y-1 = 0
y = -4 or y = 1

Answer 2

3

Answer 3

y=1/2

Answer 4

y= -1/3

Answer 5

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

Multiply through by "y"

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

Multiply through by "y + 2"

(y + 2) * 2 = [(y + 2) * (3y / (y+2))] + [(y + 2) * y]
2y + 4 = 3y + y^2 + 2y
y^2 + 3y - 4 = 0
(y + 4)(y - 1) = 0

y = -4 or 1


Check for extraneous solutions:

y = -4
(2/-4) = (3/(-4+2)) + 1
(-1/2) = (3/-2) + 1
(-1/2) = (-1/2)
not extraneous

y = 1
(2/1) = (3/(1+2)) + 1
2 = (3/3) + 1
2 = 2
not extraneous

Both y = 1 and y = -4 are solutions

Answer 6

2/y=3/y+2+1

2/y-3/y=3/y-3/y+2+1
2/y-3/y=0+2+1
-1/y=3
y(-1/y)=3(y)
-1=3y
-1/3=3y/3
-1/3=y

Answer is y= -1/3.

By the way, may I ask if you're a kid? This seems easy for an adult...

Answer 7

2/y =3/y + 3

2 = 3+ 3y

-1= 3y

y = -1/3

Definiteley the answer

Answer 8

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

Answer 9

I thing the y=1.

Answer 10

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