Solve for t
t=-z-\frac{1}{x}
x\neq 0
Solve for x
x=-\frac{1}{z+t}
t\neq -z
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1+xt+xz=0
Swap sides so that all variable terms are on the left hand side.
xt+xz=-1
Subtract 1 from both sides. Anything subtracted from zero gives its negation.
xt=-1-xz
Subtract xz from both sides.
xt=-xz-1
The equation is in standard form.
\frac{xt}{x}=\frac{-xz-1}{x}
Divide both sides by x.
t=\frac{-xz-1}{x}
Dividing by x undoes the multiplication by x.
t=-z-\frac{1}{x}
Divide -1-xz by x.
1+xt+xz=0
Swap sides so that all variable terms are on the left hand side.
xt+xz=-1
Subtract 1 from both sides. Anything subtracted from zero gives its negation.
\left(t+z\right)x=-1
Combine all terms containing x.
\left(z+t\right)x=-1
The equation is in standard form.
\frac{\left(z+t\right)x}{z+t}=-\frac{1}{z+t}
Divide both sides by t+z.
x=-\frac{1}{z+t}
Dividing by t+z undoes the multiplication by t+z.
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