Solve for f (complex solution)
\left\{\begin{matrix}f=\frac{1-2a}{x}\text{, }&x\neq 0\\f\in \mathrm{C}\text{, }&a=\frac{1}{2}\text{ and }x=0\end{matrix}\right.
Solve for a
a=\frac{1-fx}{2}
Solve for f
\left\{\begin{matrix}f=\frac{1-2a}{x}\text{, }&x\neq 0\\f\in \mathrm{R}\text{, }&a=\frac{1}{2}\text{ and }x=0\end{matrix}\right.
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fx=1-a-a
Subtract a from both sides.
fx=1-2a
Combine -a and -a to get -2a.
xf=1-2a
The equation is in standard form.
\frac{xf}{x}=\frac{1-2a}{x}
Divide both sides by x.
f=\frac{1-2a}{x}
Dividing by x undoes the multiplication by x.
fx+a+a=1
Add a to both sides.
fx+2a=1
Combine a and a to get 2a.
2a=1-fx
Subtract fx from both sides.
\frac{2a}{2}=\frac{1-fx}{2}
Divide both sides by 2.
a=\frac{1-fx}{2}
Dividing by 2 undoes the multiplication by 2.
fx=1-a-a
Subtract a from both sides.
fx=1-2a
Combine -a and -a to get -2a.
xf=1-2a
The equation is in standard form.
\frac{xf}{x}=\frac{1-2a}{x}
Divide both sides by x.
f=\frac{1-2a}{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
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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}