2/z=3/z-1/2
solve for z
multiply each term by 2z
4 = 6 - z
Can you take it from here?
z=-2 ???
No, z is 2
To solve for z in the equation 2/z = 3/z - 1/2, we can start by getting rid of the fractions.
First, we can find a common denominator for the terms on the right side of the equation, which is 2z.
The equation becomes:
2/z = (3z)/(2z) - (1)/(2)
Next, we can simplify the terms on the right side of the equation:
2/z = (3z - 1)/(2z)
Now, we can cross-multiply to eliminate the fractions:
(2)(2z) = (3z - 1)(z)
4z = 3z^2 - z
Rearranging the equation and setting it equal to zero:
3z^2 - z - 4z = 0
3z^2 - 5z = 0
We can factor out a z:
z(3z - 5) = 0
Thus, either z = 0 or (3z - 5) = 0
Solving for z in the second equation:
3z - 5 = 0
3z = 5
z = 5/3
Therefore, the solutions to the equation are z = 0 and z = 5/3.