Solve A(AADB)/A(ACDB)=AO/CO

$$\frac { A ( A A D B ) } { A ( A C D B ) } = \frac { A O } { C O }$$

Solve for A

$$A\neq 0$$

$$C\neq 0\text{ and }D\neq 0\text{ and }B\neq 0\text{ and }O\neq 0$$

Solution Steps

Variable A cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by BCDOA^{2}, the least common multiple of AACDB,CO.

$$OAAADB=BDA^{2}AO$$

Multiply A and A to get A^{2}.

$$OA^{2}ADB=BDA^{2}AO$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$OA^{3}DB=BDA^{2}AO$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$OA^{3}DB=BDA^{3}O$$

Subtract BDA^{3}O from both sides.

$$OA^{3}DB-BDA^{3}O=0$$

Combine OA^{3}DB and -BDA^{3}O to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any A.

$$A\in \mathrm{R}$$

Variable A cannot be equal to 0.

$$A\in \mathrm{R}\setminus 0$$

Solve for B

$$B\neq 0$$

$$C\neq 0\text{ and }D\neq 0\text{ and }O\neq 0\text{ and }A\neq 0$$

Solution Steps

Variable B cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by BCDOA^{2}, the least common multiple of AACDB,CO.

$$OAAADB=BDA^{2}AO$$

Multiply A and A to get A^{2}.

$$OA^{2}ADB=BDA^{2}AO$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$OA^{3}DB=BDA^{2}AO$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$OA^{3}DB=BDA^{3}O$$

Subtract BDA^{3}O from both sides.

$$OA^{3}DB-BDA^{3}O=0$$

Combine OA^{3}DB and -BDA^{3}O to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any B.

$$B\in \mathrm{R}$$

Variable B cannot be equal to 0.

$$B\in \mathrm{R}\setminus 0$$