Question

Выразить Z x(z+y)+z = 0

Answer 1

Х(z+y)+z=0
xz+xy+z=0
z+xz=-xy
z(1+x)=-xy
z=-xy/(1+x)

Answer 2

To express z in terms of x and y from the equation Zx(z+y) + z = 0, follow these steps:

Step 1: Bring the z term to one side of the equation. Zx(z + y) + z = 0 Zx(z + y) = -z

Step 2: Factor out z on the left side. z(Zx + 1) = -z

Step 3: Divide both sides by (Zx + 1) to isolate z. z = -z / (Zx + 1)

Step 4: To remove z from the denominator, multiply both sides by (Zx + 1). z(Zx + 1) = -z

Step 5: Distribute on the left side. Zx*z + z = -z

Step 6: Bring the z term to one side. Zx*z + z + z = 0

Step 7: Combine like terms. Zx*z + 2z = 0

Step 8: Factor out z on the left side. z(Zx + 2) = 0

Step 9: Now, solve for z. z = 0 or Zx + 2 = 0

If z = 0, then there's no restriction on x and y, and z can be 0.

If Zx + 2 = 0, then: Zx = -2 x = -2/Z

So, the final solutions for z in terms of x and y are:

1. z = 0
2. x = -2/Z (when Z is not equal to 0)