Solve for y (complex solution)
\left\{\begin{matrix}\\y=x-e\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
Solve for y
\left\{\begin{matrix}\\y=x-e\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
Solve for x
x=y+e
x=0
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yx=x^{2}-ex
Swap sides so that all variable terms are on the left hand side.
xy=x^{2}-ex
Reorder the terms.
\frac{xy}{x}=\frac{x\left(x-e\right)}{x}
Divide both sides by x.
y=\frac{x\left(x-e\right)}{x}
Dividing by x undoes the multiplication by x.
y=x-e
Divide x\left(x-e\right) by x.
yx=x^{2}-ex
Swap sides so that all variable terms are on the left hand side.
xy=x^{2}-ex
Reorder the terms.
\frac{xy}{x}=\frac{x\left(x-e\right)}{x}
Divide both sides by x.
y=\frac{x\left(x-e\right)}{x}
Dividing by x undoes the multiplication by x.
y=x-e
Divide x\left(x-e\right) 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
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
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