Solve for x
x=\frac{y-2}{y}
y\neq 0
Solve for y
y=\frac{2}{1-x}
x\neq 1
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2+xy=y
Swap sides so that all variable terms are on the left hand side.
xy=y-2
Subtract 2 from both sides.
yx=y-2
The equation is in standard form.
\frac{yx}{y}=\frac{y-2}{y}
Divide both sides by y.
x=\frac{y-2}{y}
Dividing by y undoes the multiplication by y.
y-xy=2
Subtract xy from both sides.
\left(1-x\right)y=2
Combine all terms containing y.
\frac{\left(1-x\right)y}{1-x}=\frac{2}{1-x}
Divide both sides by 1-x.
y=\frac{2}{1-x}
Dividing by 1-x undoes the multiplication by 1-x.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}