Resolver ABCD-ABC=DCDC

$$A B C D - A B C = D C D C$$

Resolver A

$$\left\{\begin{matrix}A=\frac{CD^{2}}{B\left(D-1\right)}\text{, }&D\neq 1\text{ and }B\neq 0\\A\in \mathrm{R}\text{, }&\left(B=0\text{ and }D=0\right)\text{ or }C=0\end{matrix}\right.$$

Pasos para resolver unha ecuación lineal

Multiplica D e D para obter D^{2}.

$$ABCD-ABC=D^{2}CC$$

Multiplica C e C para obter C^{2}.

$$ABCD-ABC=D^{2}C^{2}$$

Reordena os termos.

$$ABCD-ABC=C^{2}D^{2}$$

Combina todos os termos que conteñan A.

$$\left(BCD-BC\right)A=C^{2}D^{2}$$

Divide ambos lados entre BCD-BC.

$$\frac{\left(BCD-BC\right)A}{BCD-BC}=\frac{C^{2}D^{2}}{BCD-BC}$$

A división entre BCD-BC desfai a multiplicación por BCD-BC.

$$A=\frac{C^{2}D^{2}}{BCD-BC}$$

Divide C^{2}D^{2} entre BCD-BC.

$$A=\frac{CD^{2}}{B\left(D-1\right)}$$

Resolver B

$$\left\{\begin{matrix}B=\frac{CD^{2}}{A\left(D-1\right)}\text{, }&D\neq 1\text{ and }A\neq 0\\B\in \mathrm{R}\text{, }&\left(A=0\text{ and }D=0\right)\text{ or }C=0\end{matrix}\right.$$

Pasos para resolver unha ecuación lineal

Multiplica D e D para obter D^{2}.

$$ABCD-ABC=D^{2}CC$$

Multiplica C e C para obter C^{2}.

$$ABCD-ABC=D^{2}C^{2}$$

Reordena os termos.

$$ABCD-ABC=C^{2}D^{2}$$

Combina todos os termos que conteñan B.

$$\left(ACD-AC\right)B=C^{2}D^{2}$$

Divide ambos lados entre ACD-AC.

$$\frac{\left(ACD-AC\right)B}{ACD-AC}=\frac{C^{2}D^{2}}{ACD-AC}$$

A división entre ACD-AC desfai a multiplicación por ACD-AC.

$$B=\frac{C^{2}D^{2}}{ACD-AC}$$

Divide C^{2}D^{2} entre ACD-AC.

$$B=\frac{CD^{2}}{A\left(D-1\right)}$$