Solve 10/2+x=30/2-x

$$\frac{ 10 }{ 2+x } = \frac{ 30 }{ 2-x }$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

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

$$\left(x-2\right)\times 10=-\left(2+x\right)\times 30$$

Use the distributive property to multiply x-2 by 10.

$$10x-20=-\left(2+x\right)\times 30$$

Multiply -1 and 30 to get -30.

$$10x-20=-30\left(2+x\right)$$

Use the distributive property to multiply -30 by 2+x.

$$10x-20=-60-30x$$

Add 30x to both sides.

$$10x-20+30x=-60$$

Combine 10x and 30x to get 40x.

$$40x-20=-60$$

Add 20 to both sides.

$$40x=-60+20$$

Add -60 and 20 to get -40.

$$40x=-40$$

Divide both sides by 40.

$$x=\frac{-40}{40}$$

Divide -40 by 40 to get -1.

$$x=-1$$