Solve for B (complex solution)
\left\{\begin{matrix}B=-\frac{L_{2}x}{2yy_{1}}\text{, }&y\neq 0\text{ and }y_{1}\neq 0\\B\in \mathrm{C}\text{, }&\left(L_{2}=0\text{ and }y=0\right)\text{ or }\left(x=0\text{ and }y=0\right)\text{ or }\left(x=0\text{ and }y_{1}=0\text{ and }y\neq 0\right)\text{ or }\left(L_{2}=0\text{ and }y_{1}=0\text{ and }y\neq 0\right)\end{matrix}\right.
Solve for L_2 (complex solution)
\left\{\begin{matrix}L_{2}=-\frac{2Byy_{1}}{x}\text{, }&x\neq 0\\L_{2}\in \mathrm{C}\text{, }&\left(B=0\text{ or }y_{1}=0\text{ or }y=0\right)\text{ and }x=0\end{matrix}\right.
Solve for B
\left\{\begin{matrix}B=-\frac{L_{2}x}{2yy_{1}}\text{, }&y\neq 0\text{ and }y_{1}\neq 0\\B\in \mathrm{R}\text{, }&\left(L_{2}=0\text{ and }y=0\right)\text{ or }\left(x=0\text{ and }y=0\right)\text{ or }\left(x=0\text{ and }y_{1}=0\text{ and }y\neq 0\right)\text{ or }\left(L_{2}=0\text{ and }y_{1}=0\text{ and }y\neq 0\right)\end{matrix}\right.
Solve for L_2
\left\{\begin{matrix}L_{2}=-\frac{2Byy_{1}}{x}\text{, }&x\neq 0\\L_{2}\in \mathrm{R}\text{, }&\left(B=0\text{ or }y_{1}=0\text{ or }y=0\right)\text{ and }x=0\end{matrix}\right.
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L_{2}x+2By_{1}y=0
Multiply both sides of the equation by 2.
2By_{1}y=-L_{2}x
Subtract L_{2}x from both sides. Anything subtracted from zero gives its negation.
2Byy_{1}=-L_{2}x
Reorder the terms.
2yy_{1}B=-L_{2}x
The equation is in standard form.
\frac{2yy_{1}B}{2yy_{1}}=-\frac{L_{2}x}{2yy_{1}}
Divide both sides by 2yy_{1}.
B=-\frac{L_{2}x}{2yy_{1}}
Dividing by 2yy_{1} undoes the multiplication by 2yy_{1}.
L_{2}x+2By_{1}y=0
Multiply both sides of the equation by 2.
L_{2}x=-2By_{1}y
Subtract 2By_{1}y from both sides. Anything subtracted from zero gives its negation.
xL_{2}=-2Byy_{1}
The equation is in standard form.
\frac{xL_{2}}{x}=-\frac{2Byy_{1}}{x}
Divide both sides by x.
L_{2}=-\frac{2Byy_{1}}{x}
Dividing by x undoes the multiplication by x.
L_{2}x+2By_{1}y=0
Multiply both sides of the equation by 2.
2By_{1}y=-L_{2}x
Subtract L_{2}x from both sides. Anything subtracted from zero gives its negation.
2Byy_{1}=-L_{2}x
Reorder the terms.
2yy_{1}B=-L_{2}x
The equation is in standard form.
\frac{2yy_{1}B}{2yy_{1}}=-\frac{L_{2}x}{2yy_{1}}
Divide both sides by 2yy_{1}.
B=-\frac{L_{2}x}{2yy_{1}}
Dividing by 2yy_{1} undoes the multiplication by 2yy_{1}.
L_{2}x+2By_{1}y=0
Multiply both sides of the equation by 2.
L_{2}x=-2By_{1}y
Subtract 2By_{1}y from both sides. Anything subtracted from zero gives its negation.
xL_{2}=-2Byy_{1}
The equation is in standard form.
\frac{xL_{2}}{x}=-\frac{2Byy_{1}}{x}
Divide both sides by x.
L_{2}=-\frac{2Byy_{1}}{x}
Dividing by x undoes the multiplication by x.
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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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