Solve 02/20+2*x=0376/2*(108+x)

$$\frac{ 02 }{ 20+2 \times x } = \frac{ 0376 }{ 2 \times (108+x) }$$

Solve for x (complex solution)

$$x\in \mathrm{C}\setminus -10,-108$$

Solution Steps

Variable x cannot be equal to any of the values -108,-10 since division by zero is not defined. Multiply both sides of the equation by 2\left(x+10\right)\left(x+108\right), the least common multiple of 20+2x,2\left(108+x\right).

$$\left(x+108\right)\times 0\times 2=\left(x+10\right)\times 0\times 376$$

Multiply 0 and 2 to get 0.

$$\left(x+108\right)\times 0=\left(x+10\right)\times 0\times 376$$

Anything times zero gives zero.

$$0=\left(x+10\right)\times 0\times 376$$

Multiply 0 and 376 to get 0.

$$0=\left(x+10\right)\times 0$$

Anything times zero gives zero.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Variable x cannot be equal to any of the values -108,-10.

$$x\in \mathrm{C}\setminus -108,-10$$

Solve for x

$$x\in \mathrm{R}\setminus -10,-108$$

Solution Steps

Variable x cannot be equal to any of the values -108,-10 since division by zero is not defined. Multiply both sides of the equation by 2\left(x+10\right)\left(x+108\right), the least common multiple of 20+2x,2\left(108+x\right).

$$\left(x+108\right)\times 0\times 2=\left(x+10\right)\times 0\times 376$$

Multiply 0 and 2 to get 0.

$$\left(x+108\right)\times 0=\left(x+10\right)\times 0\times 376$$

Anything times zero gives zero.

$$0=\left(x+10\right)\times 0\times 376$$

Multiply 0 and 376 to get 0.

$$0=\left(x+10\right)\times 0$$

Anything times zero gives zero.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$

Variable x cannot be equal to any of the values -108,-10.

$$x\in \mathrm{R}\setminus -108,-10$$