Solve for s (complex solution)
\left\{\begin{matrix}s=0\text{, }&t\neq 0\\s\in \mathrm{C}\text{, }&t=x\text{ and }x\neq 0\end{matrix}\right.
Solve for s
\left\{\begin{matrix}s=0\text{, }&t\neq 0\\s\in \mathrm{R}\text{, }&t=x\text{ and }x\neq 0\end{matrix}\right.
Solve for t
\left\{\begin{matrix}t=x\text{, }&x\neq 0\\t\neq 0\text{, }&s=0\end{matrix}\right.
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s=\frac{sx}{t}
Express \frac{s}{t}x as a single fraction.
s-\frac{sx}{t}=0
Subtract \frac{sx}{t} from both sides.
\frac{st}{t}-\frac{sx}{t}=0
To add or subtract expressions, expand them to make their denominators the same. Multiply s times \frac{t}{t}.
\frac{st-sx}{t}=0
Since \frac{st}{t} and \frac{sx}{t} have the same denominator, subtract them by subtracting their numerators.
st-sx=0
Multiply both sides of the equation by t.
\left(t-x\right)s=0
Combine all terms containing s.
s=0
Divide 0 by -x+t.
s=\frac{sx}{t}
Express \frac{s}{t}x as a single fraction.
s-\frac{sx}{t}=0
Subtract \frac{sx}{t} from both sides.
\frac{st}{t}-\frac{sx}{t}=0
To add or subtract expressions, expand them to make their denominators the same. Multiply s times \frac{t}{t}.
\frac{st-sx}{t}=0
Since \frac{st}{t} and \frac{sx}{t} have the same denominator, subtract them by subtracting their numerators.
st-sx=0
Multiply both sides of the equation by t.
\left(t-x\right)s=0
Combine all terms containing s.
s=0
Divide 0 by -x+t.
st=sx
Variable t cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by t.
\frac{st}{s}=\frac{sx}{s}
Divide both sides by s.
t=\frac{sx}{s}
Dividing by s undoes the multiplication by s.
t=x
Divide sx by s.
t=x\text{, }t\neq 0
Variable t cannot be equal to 0.
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}