Solve for x
x=\frac{1}{y}
y\neq 0
Solve for y
y=\frac{1}{x}
x\neq 0
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1=yx
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.
yx=1
Swap sides so that all variable terms are on the left hand side.
\frac{yx}{y}=\frac{1}{y}
Divide both sides by y.
x=\frac{1}{y}
Dividing by y undoes the multiplication by y.
x=\frac{1}{y}\text{, }x\neq 0
Variable x cannot be equal to 0.
1=yx
Multiply both sides of the equation by x.
yx=1
Swap sides so that all variable terms are on the left hand side.
xy=1
The equation is in standard form.
\frac{xy}{x}=\frac{1}{x}
Divide both sides by x.
y=\frac{1}{x}
Dividing by x undoes the multiplication by 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
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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}