Solve for x
x=\frac{y}{1-y}
y\neq 1
Solve for y
y=\frac{x}{x+1}
x\neq -1
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x=y\left(x+1\right)
Variable x cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by x+1.
x=yx+y
Use the distributive property to multiply y by x+1.
x-yx=y
Subtract yx from both sides.
\left(1-y\right)x=y
Combine all terms containing x.
\frac{\left(1-y\right)x}{1-y}=\frac{y}{1-y}
Divide both sides by -y+1.
x=\frac{y}{1-y}
Dividing by -y+1 undoes the multiplication by -y+1.
x=\frac{y}{1-y}\text{, }x\neq -1
Variable x cannot be equal to -1.
x=y\left(x+1\right)
Multiply both sides of the equation by x+1.
x=yx+y
Use the distributive property to multiply y by x+1.
yx+y=x
Swap sides so that all variable terms are on the left hand side.
\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.
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}