Solve for A (complex solution)
\left\{\begin{matrix}A=\frac{fx\left(x^{2}-9\right)}{1-x}\text{, }&x\neq 1\text{ and }x\neq -3\text{ and }x\neq 3\\A\in \mathrm{C}\text{, }&f=0\text{ and }x=1\end{matrix}\right.
Solve for f (complex solution)
\left\{\begin{matrix}f=-\frac{A\left(x-1\right)}{x\left(x^{2}-9\right)}\text{, }&x\neq -3\text{ and }x\neq 3\text{ and }x\neq 0\\f\in \mathrm{C}\text{, }&A=0\text{ and }x=0\end{matrix}\right.
Solve for A
\left\{\begin{matrix}A=\frac{fx\left(x^{2}-9\right)}{1-x}\text{, }&x\neq 1\text{ and }|x|\neq 3\\A\in \mathrm{R}\text{, }&f=0\text{ and }x=1\end{matrix}\right.
Solve for f
\left\{\begin{matrix}f=-\frac{A\left(x-1\right)}{x\left(x^{2}-9\right)}\text{, }&x\neq 0\text{ and }|x|\neq 3\\f\in \mathrm{R}\text{, }&A=0\text{ and }x=0\end{matrix}\right.
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fx\left(x-3\right)\left(x+3\right)=\left(1-x\right)A
Multiply both sides of the equation by \left(x-3\right)\left(x+3\right).
\left(fx^{2}-3fx\right)\left(x+3\right)=\left(1-x\right)A
Use the distributive property to multiply fx by x-3.
fx^{3}-9fx=\left(1-x\right)A
Use the distributive property to multiply fx^{2}-3fx by x+3 and combine like terms.
fx^{3}-9fx=A-xA
Use the distributive property to multiply 1-x by A.
A-xA=fx^{3}-9fx
Swap sides so that all variable terms are on the left hand side.
\left(1-x\right)A=fx^{3}-9fx
Combine all terms containing A.
\frac{\left(1-x\right)A}{1-x}=\frac{fx\left(x^{2}-9\right)}{1-x}
Divide both sides by 1-x.
A=\frac{fx\left(x^{2}-9\right)}{1-x}
Dividing by 1-x undoes the multiplication by 1-x.
fx\left(x-3\right)\left(x+3\right)=\left(1-x\right)A
Multiply both sides of the equation by \left(x-3\right)\left(x+3\right).
\left(fx^{2}-3fx\right)\left(x+3\right)=\left(1-x\right)A
Use the distributive property to multiply fx by x-3.
fx^{3}-9xf=\left(1-x\right)A
Use the distributive property to multiply fx^{2}-3fx by x+3 and combine like terms.
fx^{3}-9xf=A-xA
Use the distributive property to multiply 1-x by A.
\left(x^{3}-9x\right)f=A-xA
Combine all terms containing f.
\left(x^{3}-9x\right)f=A-Ax
The equation is in standard form.
\frac{\left(x^{3}-9x\right)f}{x^{3}-9x}=\frac{A-Ax}{x^{3}-9x}
Divide both sides by x^{3}-9x.
f=\frac{A-Ax}{x^{3}-9x}
Dividing by x^{3}-9x undoes the multiplication by x^{3}-9x.
f=\frac{A\left(1-x\right)}{x\left(x^{2}-9\right)}
Divide A-Ax by x^{3}-9x.
fx\left(x-3\right)\left(x+3\right)=\left(1-x\right)A
Multiply both sides of the equation by \left(x-3\right)\left(x+3\right).
\left(fx^{2}-3fx\right)\left(x+3\right)=\left(1-x\right)A
Use the distributive property to multiply fx by x-3.
fx^{3}-9fx=\left(1-x\right)A
Use the distributive property to multiply fx^{2}-3fx by x+3 and combine like terms.
fx^{3}-9fx=A-xA
Use the distributive property to multiply 1-x by A.
A-xA=fx^{3}-9fx
Swap sides so that all variable terms are on the left hand side.
\left(1-x\right)A=fx^{3}-9fx
Combine all terms containing A.
\frac{\left(1-x\right)A}{1-x}=\frac{fx\left(x^{2}-9\right)}{1-x}
Divide both sides by 1-x.
A=\frac{fx\left(x^{2}-9\right)}{1-x}
Dividing by 1-x undoes the multiplication by 1-x.
fx\left(x-3\right)\left(x+3\right)=\left(1-x\right)A
Multiply both sides of the equation by \left(x-3\right)\left(x+3\right).
\left(fx^{2}-3fx\right)\left(x+3\right)=\left(1-x\right)A
Use the distributive property to multiply fx by x-3.
fx^{3}-9xf=\left(1-x\right)A
Use the distributive property to multiply fx^{2}-3fx by x+3 and combine like terms.
fx^{3}-9xf=A-xA
Use the distributive property to multiply 1-x by A.
\left(x^{3}-9x\right)f=A-xA
Combine all terms containing f.
\left(x^{3}-9x\right)f=A-Ax
The equation is in standard form.
\frac{\left(x^{3}-9x\right)f}{x^{3}-9x}=\frac{A-Ax}{x^{3}-9x}
Divide both sides by x^{3}-9x.
f=\frac{A-Ax}{x^{3}-9x}
Dividing by x^{3}-9x undoes the multiplication by x^{3}-9x.
f=\frac{A\left(1-x\right)}{x\left(x^{2}-9\right)}
Divide A-Ax by x^{3}-9x.
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Simultaneous equation
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Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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