Solve for a (complex solution)
a\in \mathrm{C}
c\neq 0
Solve for b (complex solution)
b\in \mathrm{C}
c\neq 0
Solve for a
a\in \mathrm{R}
c\neq 0
Solve for b
b\in \mathrm{R}
c\neq 0
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a+b=a+b
Multiply both sides of the equation by c.
a+b-a=b
Subtract a from both sides.
b=b
Combine a and -a to get 0.
\text{true}
Reorder the terms.
a\in \mathrm{C}
This is true for any a.
a+b=a+b
Multiply both sides of the equation by c.
a+b-b=a
Subtract b from both sides.
a=a
Combine b and -b to get 0.
\text{true}
Reorder the terms.
b\in \mathrm{C}
This is true for any b.
a+b=a+b
Multiply both sides of the equation by c.
a+b-a=b
Subtract a from both sides.
b=b
Combine a and -a to get 0.
\text{true}
Reorder the terms.
a\in \mathrm{R}
This is true for any a.
a+b=a+b
Multiply both sides of the equation by c.
a+b-b=a
Subtract b from both sides.
a=a
Combine b and -b to get 0.
\text{true}
Reorder the terms.
b\in \mathrm{R}
This is true for any b.
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}