Solve for A (complex solution)
\left\{\begin{matrix}A=\frac{CD^{2}}{B\left(D-1\right)}\text{, }&D\neq 1\text{ and }B\neq 0\\A\in \mathrm{C}\text{, }&\left(B=0\text{ and }D=0\right)\text{ or }C=0\end{matrix}\right.
Solve for B (complex solution)
\left\{\begin{matrix}B=\frac{CD^{2}}{A\left(D-1\right)}\text{, }&D\neq 1\text{ and }A\neq 0\\B\in \mathrm{C}\text{, }&\left(A=0\text{ and }D=0\right)\text{ or }C=0\end{matrix}\right.
Solve for A
\left\{\begin{matrix}A=\frac{CD^{2}}{B\left(D-1\right)}\text{, }&D\neq 1\text{ and }B\neq 0\\A\in \mathrm{R}\text{, }&\left(B=0\text{ and }D=0\right)\text{ or }C=0\end{matrix}\right.
Solve for B
\left\{\begin{matrix}B=\frac{CD^{2}}{A\left(D-1\right)}\text{, }&D\neq 1\text{ and }A\neq 0\\B\in \mathrm{R}\text{, }&\left(A=0\text{ and }D=0\right)\text{ or }C=0\end{matrix}\right.
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ABCD-ABC=D^{2}CC
Multiply D and D to get D^{2}.
ABCD-ABC=D^{2}C^{2}
Multiply C and C to get C^{2}.
ABCD-ABC=C^{2}D^{2}
Reorder the terms.
\left(BCD-BC\right)A=C^{2}D^{2}
Combine all terms containing A.
\frac{\left(BCD-BC\right)A}{BCD-BC}=\frac{C^{2}D^{2}}{BCD-BC}
Divide both sides by BCD-BC.
A=\frac{C^{2}D^{2}}{BCD-BC}
Dividing by BCD-BC undoes the multiplication by BCD-BC.
A=\frac{CD^{2}}{B\left(D-1\right)}
Divide C^{2}D^{2} by BCD-BC.
ABCD-ABC=D^{2}CC
Multiply D and D to get D^{2}.
ABCD-ABC=D^{2}C^{2}
Multiply C and C to get C^{2}.
ABCD-ABC=C^{2}D^{2}
Reorder the terms.
\left(ACD-AC\right)B=C^{2}D^{2}
Combine all terms containing B.
\frac{\left(ACD-AC\right)B}{ACD-AC}=\frac{C^{2}D^{2}}{ACD-AC}
Divide both sides by ACD-AC.
B=\frac{C^{2}D^{2}}{ACD-AC}
Dividing by ACD-AC undoes the multiplication by ACD-AC.
B=\frac{CD^{2}}{A\left(D-1\right)}
Divide C^{2}D^{2} by ACD-AC.
ABCD-ABC=D^{2}CC
Multiply D and D to get D^{2}.
ABCD-ABC=D^{2}C^{2}
Multiply C and C to get C^{2}.
ABCD-ABC=C^{2}D^{2}
Reorder the terms.
\left(BCD-BC\right)A=C^{2}D^{2}
Combine all terms containing A.
\frac{\left(BCD-BC\right)A}{BCD-BC}=\frac{C^{2}D^{2}}{BCD-BC}
Divide both sides by BCD-BC.
A=\frac{C^{2}D^{2}}{BCD-BC}
Dividing by BCD-BC undoes the multiplication by BCD-BC.
A=\frac{CD^{2}}{B\left(D-1\right)}
Divide C^{2}D^{2} by BCD-BC.
ABCD-ABC=D^{2}CC
Multiply D and D to get D^{2}.
ABCD-ABC=D^{2}C^{2}
Multiply C and C to get C^{2}.
ABCD-ABC=C^{2}D^{2}
Reorder the terms.
\left(ACD-AC\right)B=C^{2}D^{2}
Combine all terms containing B.
\frac{\left(ACD-AC\right)B}{ACD-AC}=\frac{C^{2}D^{2}}{ACD-AC}
Divide both sides by ACD-AC.
B=\frac{C^{2}D^{2}}{ACD-AC}
Dividing by ACD-AC undoes the multiplication by ACD-AC.
B=\frac{CD^{2}}{A\left(D-1\right)}
Divide C^{2}D^{2} by ACD-AC.
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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}