Solve for a (complex solution)
\left\{\begin{matrix}a=\frac{\sqrt{\frac{x^{2}+4}{x+3}}}{fgx}\text{, }&x\neq 0\text{ and }g\neq 0\text{ and }f\neq 0\text{ and }x\neq -3\\a\in \mathrm{C}\text{, }&\left(x=2i\text{ and }g=0\right)\text{ or }\left(x=-2i\text{ and }g=0\right)\text{ or }\left(f=0\text{ and }g\neq 0\text{ and }x=-2i\right)\text{ or }\left(f=0\text{ and }g\neq 0\text{ and }x=2i\right)\end{matrix}\right.
Solve for f (complex solution)
\left\{\begin{matrix}f=\frac{\sqrt{\frac{x^{2}+4}{x+3}}}{agx}\text{, }&x\neq 0\text{ and }g\neq 0\text{ and }a\neq 0\text{ and }x\neq -3\\f\in \mathrm{C}\text{, }&\left(x=2i\text{ and }g=0\right)\text{ or }\left(x=-2i\text{ and }g=0\right)\text{ or }\left(a=0\text{ and }g\neq 0\text{ and }x=-2i\right)\text{ or }\left(a=0\text{ and }g\neq 0\text{ and }x=2i\right)\end{matrix}\right.
Solve for a
a=\frac{\sqrt{\frac{x^{2}+4}{x+3}}}{fgx}
x\neq 0\text{ and }g\neq 0\text{ and }f\neq 0\text{ and }x>-3
Solve for f
f=\frac{\sqrt{\frac{x^{2}+4}{x+3}}}{agx}
x\neq 0\text{ and }g\neq 0\text{ and }a\neq 0\text{ and }x>-3
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Linear Equation
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( f a g ) ( x ) = \sqrt { \frac { x ^ { 2 } + 4 } { 3 + x } }
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fgxa=\sqrt{\frac{x^{2}+4}{x+3}}
The equation is in standard form.
\frac{fgxa}{fgx}=\frac{\sqrt{\frac{x^{2}+4}{x+3}}}{fgx}
Divide both sides by fgx.
a=\frac{\sqrt{\frac{x^{2}+4}{x+3}}}{fgx}
Dividing by fgx undoes the multiplication by fgx.
agxf=\sqrt{\frac{x^{2}+4}{x+3}}
The equation is in standard form.
\frac{agxf}{agx}=\frac{\sqrt{\frac{x^{2}+4}{x+3}}}{agx}
Divide both sides by agx.
f=\frac{\sqrt{\frac{x^{2}+4}{x+3}}}{agx}
Dividing by agx undoes the multiplication by agx.
fgxa=\sqrt{\frac{x^{2}+4}{x+3}}
The equation is in standard form.
\frac{fgxa}{fgx}=\frac{\sqrt{x^{2}+4}}{\sqrt{x+3}fgx}
Divide both sides by fgx.
a=\frac{\sqrt{x^{2}+4}}{\sqrt{x+3}fgx}
Dividing by fgx undoes the multiplication by fgx.
agxf=\sqrt{\frac{x^{2}+4}{x+3}}
The equation is in standard form.
\frac{agxf}{agx}=\frac{\sqrt{x^{2}+4}}{\sqrt{x+3}agx}
Divide both sides by agx.
f=\frac{\sqrt{x^{2}+4}}{\sqrt{x+3}agx}
Dividing by agx undoes the multiplication by agx.
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