Solve for A
A\neq 0
D\neq 0\text{ and }C\neq 0
Solve for B
B\in \mathrm{R}
A\neq 0\text{ and }C\neq 0\text{ and }D\neq 0
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DAB=ABD
Variable A cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by ACD, the least common multiple of AC,DC.
DAB-ABD=0
Subtract ABD from both sides.
0=0
Combine DAB and -ABD to get 0.
\text{true}
Compare 0 and 0.
A\in \mathrm{R}
This is true for any A.
A\in \mathrm{R}\setminus 0
Variable A cannot be equal to 0.
DAB=ABD
Multiply both sides of the equation by ACD, the least common multiple of AC,DC.
DAB-ABD=0
Subtract ABD from both sides.
0=0
Combine DAB and -ABD to get 0.
\text{true}
Compare 0 and 0.
B\in \mathrm{R}
This is true for any B.
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}