Transpose (x) when z=square root of x/x+y?

To transpose the equation when z = sqrt(x/(x+y), we need to isolate x on one side of the equation.

First, square both sides of the equation to get rid of the square root:

z^2 = x/(x+y)

Next, multiply both sides by (x+y) to get rid of the denominator:

z^2(x+y) = x

Expand the left side:

z^2x + z^2y = x

Now, isolate x on one side:

z^2x - x = -z^2y

Factor out x:

x(z^2 - 1) = -z^2y

Divide by (z^2 - 1) to solve for x:

x = -z^2y / (z^2 - 1)

Therefore, the transposed equation is x = -z^2y / (z^2 - 1).

$$z=\sqrt{\frac{x}{xy}}$$

$$z=\sqrt{\frac{1}{y}}$$

$$z=\frac{1}{\sqrt{y}}$$

$$z=\frac{1}{\sqrt{\frac{1}{x}}}$$

$$z=\sqrt{x}$$

$$x=z^2$$