What is the answer to solvefor x,(x+y+z)/x-y=z ?

The answer to solvefor x,(x+y+z)/x-y=z is x=(-y-z)/(1-z-y);\quad y\ne-z+1

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solvefor x,(x+y+z)/x-y=z

solve for

x, \frac{x + y + z}{x} - y = z

x = \frac{- y - z}{1 - z - y}; y \neq = - z + 1

Solution steps

\frac{x + y + z}{x} - y = z

Move

y

to the right side

\frac{x + y + z}{x} = z + y

Multiply both sides by

x

x + y + z = z x + y x

Move

y

to the right side

x + z = z x + y x - y

Move

z

to the right side

x = z x + y x - y - z

Subtract

z x + y x

from both sides

x - (z x + y x) = z x + y x - y - z - (z x + y x)

Simplify

x - x z - x y = - y - z

Factor

x - x z - x y : x (1 - z - y)

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

Divide both sides by

1 - z - y; y \neq = - z + 1

x = \frac{- y - z}{1 - z - y}; y \neq = - z + 1

\frac{x + 6}{x - 3} = \frac{4}{7}

\frac{2}{x - 1} - \frac{3}{x} = 2

\frac{x}{x + 3} = \frac{2}{x + 5}

y + \frac{1}{y} - 22 = 0

\frac{3}{9} = \frac{3}{x + 2}

What is the answer to solvefor x,(x+y+z)/x-y=z ?
The answer to solvefor x,(x+y+z)/x-y=z is x=(-y-z)/(1-z-y);\quad y\ne-z+1