Solve for f (complex solution)
\left\{\begin{matrix}f=\frac{2x^{2}+4x+5}{nx}\text{, }&x\neq 0\text{ and }n\neq 0\\f\in \mathrm{C}\text{, }&\left(x=\frac{\sqrt{6}i}{2}-1\text{ or }x=-\frac{\sqrt{6}i}{2}-1\right)\text{ and }n=0\end{matrix}\right.
Solve for n (complex solution)
\left\{\begin{matrix}n=\frac{2x^{2}+4x+5}{fx}\text{, }&x\neq 0\text{ and }f\neq 0\\n\in \mathrm{C}\text{, }&\left(x=\frac{\sqrt{6}i}{2}-1\text{ or }x=-\frac{\sqrt{6}i}{2}-1\right)\text{ and }f=0\end{matrix}\right.
Solve for f
f=\frac{2x^{2}+4x+5}{nx}
x\neq 0\text{ and }n\neq 0
Solve for n
n=\frac{2x^{2}+4x+5}{fx}
x\neq 0\text{ and }f\neq 0
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nxf=2x^{2}+4x+5
The equation is in standard form.
\frac{nxf}{nx}=\frac{2x^{2}+4x+5}{nx}
Divide both sides by nx.
f=\frac{2x^{2}+4x+5}{nx}
Dividing by nx undoes the multiplication by nx.
fxn=2x^{2}+4x+5
The equation is in standard form.
\frac{fxn}{fx}=\frac{2x^{2}+4x+5}{fx}
Divide both sides by fx.
n=\frac{2x^{2}+4x+5}{fx}
Dividing by fx undoes the multiplication by fx.
nxf=2x^{2}+4x+5
The equation is in standard form.
\frac{nxf}{nx}=\frac{2x^{2}+4x+5}{nx}
Divide both sides by nx.
f=\frac{2x^{2}+4x+5}{nx}
Dividing by nx undoes the multiplication by nx.
fxn=2x^{2}+4x+5
The equation is in standard form.
\frac{fxn}{fx}=\frac{2x^{2}+4x+5}{fx}
Divide both sides by fx.
n=\frac{2x^{2}+4x+5}{fx}
Dividing by fx undoes the multiplication by fx.
Examples
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\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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