Solve for m (complex solution)
\left\{\begin{matrix}m=\frac{p\left(q-1\right)}{q}\text{, }&q\neq 0\\m\in \mathrm{C}\text{, }&p=0\text{ and }q=0\end{matrix}\right.
Solve for p (complex solution)
\left\{\begin{matrix}p=-\frac{mq}{1-q}\text{, }&q\neq 1\\p\in \mathrm{C}\text{, }&m=0\text{ and }q=1\end{matrix}\right.
Solve for m
\left\{\begin{matrix}m=\frac{p\left(q-1\right)}{q}\text{, }&q\neq 0\\m\in \mathrm{R}\text{, }&p=0\text{ and }q=0\end{matrix}\right.
Solve for p
\left\{\begin{matrix}p=-\frac{mq}{1-q}\text{, }&q\neq 1\\p\in \mathrm{R}\text{, }&m=0\text{ and }q=1\end{matrix}\right.
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qm=pq-p
Subtract p from both sides.
\frac{qm}{q}=\frac{p\left(q-1\right)}{q}
Divide both sides by q.
m=\frac{p\left(q-1\right)}{q}
Dividing by q undoes the multiplication by q.
p+qm-pq=0
Subtract pq from both sides.
p-pq=-qm
Subtract qm from both sides. Anything subtracted from zero gives its negation.
-pq+p=-mq
Reorder the terms.
\left(-q+1\right)p=-mq
Combine all terms containing p.
\left(1-q\right)p=-mq
The equation is in standard form.
\frac{\left(1-q\right)p}{1-q}=-\frac{mq}{1-q}
Divide both sides by 1-q.
p=-\frac{mq}{1-q}
Dividing by 1-q undoes the multiplication by 1-q.
qm=pq-p
Subtract p from both sides.
\frac{qm}{q}=\frac{p\left(q-1\right)}{q}
Divide both sides by q.
m=\frac{p\left(q-1\right)}{q}
Dividing by q undoes the multiplication by q.
p+qm-pq=0
Subtract pq from both sides.
p-pq=-qm
Subtract qm from both sides. Anything subtracted from zero gives its negation.
-pq+p=-mq
Reorder the terms.
\left(-q+1\right)p=-mq
Combine all terms containing p.
\left(1-q\right)p=-mq
The equation is in standard form.
\frac{\left(1-q\right)p}{1-q}=-\frac{mq}{1-q}
Divide both sides by 1-q.
p=-\frac{mq}{1-q}
Dividing by 1-q undoes the multiplication by 1-q.
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}