How would I make z the subject of the formulae:
x=y(z-y)/z
(z-y)/z = 1 - (y/z) = x/y
y/z = 1 - (x/y)= (y-x)/y
z/y = y/(y-x)
z = y^2/(y-x)
To make z the subject of the formula, we want to isolate z on one side of the equation by performing a series of algebraic manipulations. Here's how you can do it step by step:
1. Start by multiplying both sides of the equation by z to eliminate the denominator:
xz = y(z - y)
2. Expand the brackets on the right side of the equation:
xz = yz - y^2
3. Move the term yz to the left side of the equation by subtracting yz from both sides:
xz - yz = -y^2
4. Factor out z on the left side of the equation:
z(x - y) = -y^2
5. Finally, divide both sides of the equation by (x - y) to solve for z:
z = -y^2 / (x - y)
So the formula with z as the subject is z = -y^2 / (x - y).