Solve for x
x=-\frac{y}{y+1}
y\neq -1
Solve for y
y=-\frac{x}{x+1}
x\neq -1
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xy-x=2xy+y
Subtract x from both sides.
xy-x-2xy=y
Subtract 2xy from both sides.
-xy-x=y
Combine xy and -2xy to get -xy.
\left(-y-1\right)x=y
Combine all terms containing x.
\frac{\left(-y-1\right)x}{-y-1}=\frac{y}{-y-1}
Divide both sides by -y-1.
x=\frac{y}{-y-1}
Dividing by -y-1 undoes the multiplication by -y-1.
x=-\frac{y}{y+1}
Divide y by -y-1.
xy-2xy=x+y
Subtract 2xy from both sides.
-xy=x+y
Combine xy and -2xy to get -xy.
-xy-y=x
Subtract y from both sides.
\left(-x-1\right)y=x
Combine all terms containing y.
\frac{\left(-x-1\right)y}{-x-1}=\frac{x}{-x-1}
Divide both sides by -x-1.
y=\frac{x}{-x-1}
Dividing by -x-1 undoes the multiplication by -x-1.
y=-\frac{x}{x+1}
Divide x by -x-1.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
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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}