Solve for K (complex solution)
\left\{\begin{matrix}K=\frac{3x}{2R}-1\text{, }&R\neq 0\\K\in \mathrm{C}\text{, }&x=0\text{ and }R=0\end{matrix}\right.
Solve for R (complex solution)
\left\{\begin{matrix}R=\frac{3x}{2\left(K+1\right)}\text{, }&K\neq -1\\R\in \mathrm{C}\text{, }&x=0\text{ and }K=-1\end{matrix}\right.
Solve for K
\left\{\begin{matrix}K=\frac{3x}{2R}-1\text{, }&R\neq 0\\K\in \mathrm{R}\text{, }&x=0\text{ and }R=0\end{matrix}\right.
Solve for R
\left\{\begin{matrix}R=\frac{3x}{2\left(K+1\right)}\text{, }&K\neq -1\\R\in \mathrm{R}\text{, }&x=0\text{ and }K=-1\end{matrix}\right.
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3x-2R=2KR
Multiply both sides of the equation by 2.
2KR=3x-2R
Swap sides so that all variable terms are on the left hand side.
2RK=3x-2R
The equation is in standard form.
\frac{2RK}{2R}=\frac{3x-2R}{2R}
Divide both sides by 2R.
K=\frac{3x-2R}{2R}
Dividing by 2R undoes the multiplication by 2R.
K=\frac{3x}{2R}-1
Divide 3x-2R by 2R.
3x-2R=2KR
Multiply both sides of the equation by 2.
3x-2R-2KR=0
Subtract 2KR from both sides.
-2R-2KR=-3x
Subtract 3x from both sides. Anything subtracted from zero gives its negation.
\left(-2-2K\right)R=-3x
Combine all terms containing R.
\left(-2K-2\right)R=-3x
The equation is in standard form.
\frac{\left(-2K-2\right)R}{-2K-2}=-\frac{3x}{-2K-2}
Divide both sides by -2-2K.
R=-\frac{3x}{-2K-2}
Dividing by -2-2K undoes the multiplication by -2-2K.
R=\frac{3x}{2\left(K+1\right)}
Divide -3x by -2-2K.
3x-2R=2KR
Multiply both sides of the equation by 2.
2KR=3x-2R
Swap sides so that all variable terms are on the left hand side.
2RK=3x-2R
The equation is in standard form.
\frac{2RK}{2R}=\frac{3x-2R}{2R}
Divide both sides by 2R.
K=\frac{3x-2R}{2R}
Dividing by 2R undoes the multiplication by 2R.
K=\frac{3x}{2R}-1
Divide 3x-2R by 2R.
3x-2R=2KR
Multiply both sides of the equation by 2.
3x-2R-2KR=0
Subtract 2KR from both sides.
-2R-2KR=-3x
Subtract 3x from both sides. Anything subtracted from zero gives its negation.
\left(-2-2K\right)R=-3x
Combine all terms containing R.
\left(-2K-2\right)R=-3x
The equation is in standard form.
\frac{\left(-2K-2\right)R}{-2K-2}=-\frac{3x}{-2K-2}
Divide both sides by -2-2K.
R=-\frac{3x}{-2K-2}
Dividing by -2-2K undoes the multiplication by -2-2K.
R=\frac{3x}{2\left(K+1\right)}
Divide -3x by -2-2K.
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}