Solve for F (complex solution)
\left\{\begin{matrix}F=\frac{2}{x-3}\text{, }&x\neq -3\text{ and }x\neq 3\\F\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
Solve for F
\left\{\begin{matrix}F=\frac{2}{x-3}\text{, }&|x|\neq 3\\F\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=3+\frac{2}{F}\text{, }&F\neq -\frac{1}{3}\text{ and }F\neq 0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=3+\frac{2}{F}\text{, }&F\neq 0\text{ and }F\neq -\frac{1}{3}\end{matrix}\right.
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Fx\left(x-3\right)\left(x+3\right)=2x\left(x+3\right)
Multiply both sides of the equation by \left(x-3\right)\left(x+3\right).
\left(Fx^{2}-3Fx\right)\left(x+3\right)=2x\left(x+3\right)
Use the distributive property to multiply Fx by x-3.
Fx^{3}-9Fx=2x\left(x+3\right)
Use the distributive property to multiply Fx^{2}-3Fx by x+3 and combine like terms.
Fx^{3}-9Fx=2x^{2}+6x
Use the distributive property to multiply 2x by x+3.
\left(x^{3}-9x\right)F=2x^{2}+6x
Combine all terms containing F.
\frac{\left(x^{3}-9x\right)F}{x^{3}-9x}=\frac{2x\left(x+3\right)}{x^{3}-9x}
Divide both sides by x^{3}-9x.
F=\frac{2x\left(x+3\right)}{x^{3}-9x}
Dividing by x^{3}-9x undoes the multiplication by x^{3}-9x.
F=\frac{2}{x-3}
Divide 2x\left(3+x\right) by x^{3}-9x.
Fx\left(x-3\right)\left(x+3\right)=2x\left(x+3\right)
Multiply both sides of the equation by \left(x-3\right)\left(x+3\right).
\left(Fx^{2}-3Fx\right)\left(x+3\right)=2x\left(x+3\right)
Use the distributive property to multiply Fx by x-3.
Fx^{3}-9Fx=2x\left(x+3\right)
Use the distributive property to multiply Fx^{2}-3Fx by x+3 and combine like terms.
Fx^{3}-9Fx=2x^{2}+6x
Use the distributive property to multiply 2x by x+3.
\left(x^{3}-9x\right)F=2x^{2}+6x
Combine all terms containing F.
\frac{\left(x^{3}-9x\right)F}{x^{3}-9x}=\frac{2x\left(x+3\right)}{x^{3}-9x}
Divide both sides by x^{3}-9x.
F=\frac{2x\left(x+3\right)}{x^{3}-9x}
Dividing by x^{3}-9x undoes the multiplication by x^{3}-9x.
F=\frac{2}{x-3}
Divide 2x\left(3+x\right) by x^{3}-9x.
Examples
Quadratic equation
{ 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}