Solve for X
\left\{\begin{matrix}X=\frac{Z}{y}\text{, }&y\neq 0\\X\in \mathrm{R}\text{, }&Z=0\text{ and }y=0\end{matrix}\right.
Solve for F
F\in \mathrm{R}
Z=Xy
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Xy+X\frac{\mathrm{d}}{\mathrm{d}x}(F)x=Z
Swap sides so that all variable terms are on the left hand side.
\left(y+\frac{\mathrm{d}}{\mathrm{d}x}(F)x\right)X=Z
Combine all terms containing X.
yX=Z
The equation is in standard form.
\frac{yX}{y}=\frac{Z}{y}
Divide both sides by y.
X=\frac{Z}{y}
Dividing by y undoes the multiplication by y.
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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