Solve for x
x=\frac{y-1}{y}
y\neq 0
Solve for y
y=-\frac{1}{x-1}
x\neq 1
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yx+1=y
Multiply both sides of the equation by y.
yx=y-1
Subtract 1 from both sides.
\frac{yx}{y}=\frac{y-1}{y}
Divide both sides by y.
x=\frac{y-1}{y}
Dividing by y undoes the multiplication by y.
yx+1=y
Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y.
yx+1-y=0
Subtract y from both sides.
yx-y=-1
Subtract 1 from both sides. Anything subtracted from zero gives its negation.
\left(x-1\right)y=-1
Combine all terms containing y.
\frac{\left(x-1\right)y}{x-1}=-\frac{1}{x-1}
Divide both sides by x-1.
y=-\frac{1}{x-1}
Dividing by x-1 undoes the multiplication by x-1.
y=-\frac{1}{x-1}\text{, }y\neq 0
Variable y cannot be equal to 0.
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}