Solve for x
x=\frac{y-1}{y+1}
y\neq -1
Solve for y
y=\frac{x+1}{1-x}
x\neq 1
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y-xy=x+1
Use the distributive property to multiply 1-x by y.
y-xy-x=1
Subtract x from both sides.
-xy-x=1-y
Subtract y from both sides.
\left(-y-1\right)x=1-y
Combine all terms containing x.
\frac{\left(-y-1\right)x}{-y-1}=\frac{1-y}{-y-1}
Divide both sides by -y-1.
x=\frac{1-y}{-y-1}
Dividing by -y-1 undoes the multiplication by -y-1.
x=-\frac{1-y}{y+1}
Divide 1-y by -y-1.
y-xy=x+1
Use the distributive property to multiply 1-x by y.
\left(1-x\right)y=x+1
Combine all terms containing y.
\frac{\left(1-x\right)y}{1-x}=\frac{x+1}{1-x}
Divide both sides by 1-x.
y=\frac{x+1}{1-x}
Dividing by 1-x undoes the multiplication by 1-x.
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
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}