Solve frac{x_{1}}{x_{1}+2}=frac{x_{2}}{x_{2}+2}

$$\frac { x _ { 1 } } { x _ { 1 } + 2 } = \frac { x _ { 2 } } { x _ { 2 } + 2 }$$

Solve for x_1

$$x_{1}=x_{2}$$

$$x_{2}\neq -2$$

Solution Steps

Variable x_{1} cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by \left(x_{1}+2\right)\left(x_{2}+2\right), the least common multiple of x_{1}+2,x_{2}+2.

$$\left(x_{2}+2\right)x_{1}=\left(x_{1}+2\right)x_{2}$$

Use the distributive property to multiply x_{2}+2 by x_{1}.

$$x_{2}x_{1}+2x_{1}=\left(x_{1}+2\right)x_{2}$$

Use the distributive property to multiply x_{1}+2 by x_{2}.

$$x_{2}x_{1}+2x_{1}=x_{1}x_{2}+2x_{2}$$

Subtract x_{1}x_{2} from both sides.

$$x_{2}x_{1}+2x_{1}-x_{1}x_{2}=2x_{2}$$

Combine x_{2}x_{1} and -x_{1}x_{2} to get 0.

$$2x_{1}=2x_{2}$$

Cancel out 2 on both sides.

$$x_{1}=x_{2}$$

Variable x_{1} cannot be equal to -2.

$$x_{1}=x_{2}\text{, }x_{1}\neq -2$$

Solve for x_2

$$x_{2}=x_{1}$$

$$x_{1}\neq -2$$

Solution Steps

Variable x_{2} cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by \left(x_{1}+2\right)\left(x_{2}+2\right), the least common multiple of x_{1}+2,x_{2}+2.

$$\left(x_{2}+2\right)x_{1}=\left(x_{1}+2\right)x_{2}$$

Use the distributive property to multiply x_{2}+2 by x_{1}.

$$x_{2}x_{1}+2x_{1}=\left(x_{1}+2\right)x_{2}$$

Use the distributive property to multiply x_{1}+2 by x_{2}.

$$x_{2}x_{1}+2x_{1}=x_{1}x_{2}+2x_{2}$$

Subtract x_{1}x_{2} from both sides.

$$x_{2}x_{1}+2x_{1}-x_{1}x_{2}=2x_{2}$$

Combine x_{2}x_{1} and -x_{1}x_{2} to get 0.

$$2x_{1}=2x_{2}$$

Swap sides so that all variable terms are on the left hand side.

$$2x_{2}=2x_{1}$$

Cancel out 2 on both sides.

$$x_{2}=x_{1}$$

Variable x_{2} cannot be equal to -2.

$$x_{2}=x_{1}\text{, }x_{2}\neq -2$$