{ f }^{ } x = \frac{ 3x }{ { x }^{ 2 } -1 }
Solve for f (complex solution)
\left\{\begin{matrix}f=\frac{3}{x^{2}-1}\text{, }&x\neq -1\text{ and }x\neq 1\\f\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
Solve for f
\left\{\begin{matrix}f=\frac{3}{x^{2}-1}\text{, }&|x|\neq 1\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=-\sqrt{\frac{f+3}{f}}\text{; }x=\sqrt{\frac{f+3}{f}}\text{, }&f\neq 0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\sqrt{\frac{f+3}{f}}\text{; }x=-\sqrt{\frac{f+3}{f}}\text{, }&f\leq -3\text{ or }f>0\end{matrix}\right.
Graph
Share
Copied to clipboard
f^{1}x\left(x-1\right)\left(x+1\right)=3x
Multiply both sides of the equation by \left(x-1\right)\left(x+1\right).
fx\left(x-1\right)\left(x+1\right)=3x
Calculate f to the power of 1 and get f.
\left(fx^{2}-fx\right)\left(x+1\right)=3x
Use the distributive property to multiply fx by x-1.
fx^{3}-fx=3x
Use the distributive property to multiply fx^{2}-fx by x+1 and combine like terms.
\left(x^{3}-x\right)f=3x
Combine all terms containing f.
\frac{\left(x^{3}-x\right)f}{x^{3}-x}=\frac{3x}{x^{3}-x}
Divide both sides by x^{3}-x.
f=\frac{3x}{x^{3}-x}
Dividing by x^{3}-x undoes the multiplication by x^{3}-x.
f=\frac{3}{x^{2}-1}
Divide 3x by x^{3}-x.
f^{1}x\left(x-1\right)\left(x+1\right)=3x
Multiply both sides of the equation by \left(x-1\right)\left(x+1\right).
fx\left(x-1\right)\left(x+1\right)=3x
Calculate f to the power of 1 and get f.
\left(fx^{2}-fx\right)\left(x+1\right)=3x
Use the distributive property to multiply fx by x-1.
fx^{3}-fx=3x
Use the distributive property to multiply fx^{2}-fx by x+1 and combine like terms.
\left(x^{3}-x\right)f=3x
Combine all terms containing f.
\frac{\left(x^{3}-x\right)f}{x^{3}-x}=\frac{3x}{x^{3}-x}
Divide both sides by x^{3}-x.
f=\frac{3x}{x^{3}-x}
Dividing by x^{3}-x undoes the multiplication by x^{3}-x.
f=\frac{3}{x^{2}-1}
Divide 3x by x^{3}-x.
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}