Solve for f (complex solution)
\left\{\begin{matrix}f=\frac{4x^{2}+10x+9}{gx}\text{, }&x\neq 0\text{ and }g\neq 0\\f\in \mathrm{C}\text{, }&\left(x=\frac{-5+\sqrt{11}i}{4}\text{ or }x=\frac{-\sqrt{11}i-5}{4}\right)\text{ and }g=0\end{matrix}\right.
Solve for g (complex solution)
\left\{\begin{matrix}g=\frac{4x^{2}+10x+9}{fx}\text{, }&x\neq 0\text{ and }f\neq 0\\g\in \mathrm{C}\text{, }&\left(x=\frac{-5+\sqrt{11}i}{4}\text{ or }x=\frac{-\sqrt{11}i-5}{4}\right)\text{ and }f=0\end{matrix}\right.
Solve for f
f=\frac{4x^{2}+10x+9}{gx}
x\neq 0\text{ and }g\neq 0
Solve for g
g=\frac{4x^{2}+10x+9}{fx}
x\neq 0\text{ and }f\neq 0
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gfx=4x^{2}+12x+9-2x
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+3\right)^{2}.
gfx=4x^{2}+10x+9
Combine 12x and -2x to get 10x.
gxf=4x^{2}+10x+9
The equation is in standard form.
\frac{gxf}{gx}=\frac{4x^{2}+10x+9}{gx}
Divide both sides by gx.
f=\frac{4x^{2}+10x+9}{gx}
Dividing by gx undoes the multiplication by gx.
gfx=4x^{2}+12x+9-2x
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+3\right)^{2}.
gfx=4x^{2}+10x+9
Combine 12x and -2x to get 10x.
fxg=4x^{2}+10x+9
The equation is in standard form.
\frac{fxg}{fx}=\frac{4x^{2}+10x+9}{fx}
Divide both sides by fx.
g=\frac{4x^{2}+10x+9}{fx}
Dividing by fx undoes the multiplication by fx.
gfx=4x^{2}+12x+9-2x
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+3\right)^{2}.
gfx=4x^{2}+10x+9
Combine 12x and -2x to get 10x.
gxf=4x^{2}+10x+9
The equation is in standard form.
\frac{gxf}{gx}=\frac{4x^{2}+10x+9}{gx}
Divide both sides by gx.
f=\frac{4x^{2}+10x+9}{gx}
Dividing by gx undoes the multiplication by gx.
gfx=4x^{2}+12x+9-2x
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+3\right)^{2}.
gfx=4x^{2}+10x+9
Combine 12x and -2x to get 10x.
fxg=4x^{2}+10x+9
The equation is in standard form.
\frac{fxg}{fx}=\frac{4x^{2}+10x+9}{fx}
Divide both sides by fx.
g=\frac{4x^{2}+10x+9}{fx}
Dividing by fx undoes the multiplication by fx.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}