Question

Solve for the variable x in terms of y and z:
xy + 2x = x - 2y + z + xz - 5xy + x^2 - x^3*y + x*y^2.

Answer 1

To solve for x in terms of y and z, we need to group the terms involving x together:

xy + 2x - x + 2y + xz - z + 5xy - x^2 + x^3*y - x*y^2 = 0.

Combine like terms:

2xy + x + 2y + xz - z - x^2 + x^3*y - x*y^2 = 0.

Rearrange the equation:

x^3*y - x^2 + 2xy - x*y^2 + x + 2y + xz - z = 0.

Factor out x:

x(x^2*y - x + 2y - y^2 + 2 + z) = 0.

Solve for x:

x = 0 or x = -(2y + z - y^2 + 2) / (x^2*y - 1).

Therefore, x can be expressed in terms of y and z as x = -(2y + z - y^2 + 2) / (x^2*y - 1) where x is not equal to 0. Or x = 0.