1/x + 2/y = 3/z solve for x?

Question

10 points for best answer

Answer 1

subtract 2/y from both sides to get 1/x = 3/z -2/y
find common denominator 1/x = (3y-2z)/ yz then flip both sides to get x = yz/(3y-2z)

Answer 2

Rather than directly going after the LCD, I want to separate the x terms on one side of the equal sign and all the rest on the other. Thus, we subtract 2/y from both sides

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

then we get:

1/x = 3/z - 2/y

now, we do the operation on the right side by using the lowest common denominator yz

1/x = 3y/yz - 2z/yz

then we group the terms on the right side

1/x = (3y - 2z) / yz

Here is the tricky part!!!

if x = {answer}, then {1/x} = {1/answer} and vice versa.

This is valid on all space except x=0 or 1/x = 0 ( x goes to infinity).

the answer is

x = yz /(3y - 2z)

this answer is valid everywhere EXCEPT: y = 0, x = 0 or 3y = 2z

Answer 3

First multiply everything by x: 1 + 2x/y = 3x/z
Now, isolate the x terms: 1 = 3x/z - 2x/y
Factor an x out of the right side: 1 = x*(3/x-2/y)
Now divide both sides by (3/x-2/y): 1/(3/x - 2/y) = x

Answer 4

so which you have isolate y on one area. subtract a million/x from the left area and acceptable. 2/y=3/z-a million/x Then multiply by y to get it into the numerator. (3/z-a million/x)y=2 Divide the two factors by 3/z-a million/x and your answer would be: y=2/(3/z-a million/x)

Answer 5

y + 2x/xy = 3/z

3xy + z(y +2x)

3xy = yz + 2xz

3xy - 2xz = yz

x(3y - 2z) = yz

x= yz/(3y - 2z)

Answer 6

(y+2x)/xy = 3/z

y+2x =3xy/z

2x=(3xy/z)-y

x= [(3xy/z)-y]/2